DOCUMENT RESUME ED 358 173 UD 029 143 AUTHOR Rester, Donald TITLE an Instructional Guide Concerning the Highly Successful Teachi

DOCUMENT RESUME

ED 358 173 UD 029 143

AUTHOR Rester, Donald TITLE An Instructional Guide Concerning the Highly Successful Teaching & Motivating Practices of Jaime Escalante for the Escalante Math Project at East Los Angeles College. INSTITUTION Los Angeles County Office of Education, Downey, CA. SPONS AGENCY ARCO Foundation, Los Angeles, CA.; East Los Angeles Coll., Calif.; Ford Foundation, New York, N.Y.; National Science Foundation, Washington, D.C. PUB DATE Ma: 93 NOTE 133p.; Parts of this paper were presented at the Annual Meetings of the American Evaluation Association (Washington, DC, October 18-20, 1990), the California Educational Research Association (San Diego, CA, November 1990), the American Evaluation Association (Seattle, WA, November 5-7, 1992), and the California Educational Research Association Conference (San Francisco, CA, November 1992). PUB TYPE Guides Classroom Use Teaching Guides (For Teacher) (052) Reports Research/Technical (143) Tests/Evaluation instruments (160)

EDRS PRICE MFOI/PC06 Plus Postage. DESCRIPTORS *Academic Achievement; Curriculum F.aluation; Educationally Disadvantaged; High SC-ools; *High School Students; *Hispanic Americans; Instructional Materials; Interviews; *Mathematics Instruction; Minority Group Children; Program Descriptions; Student Evaluation of Teacher Performance; Student Motivation; Teaching Guides; Teaching Methods; Urban Education IDENTIFIERS *Escalante Jaime; Jaime Escalante Math Program; *Los Angeles City Schools CA

ABSTRACT This instructional guide, or.e product ofa large -scale research project on Jaime Escalante and his Mathematics and Science Program, describes the teaching and motivatingstrategies that he uses to bring about high academic achievementamong poor minority urban youth in Los Angeles (California). The firstpart of five describes a pilot test in whicha colleague and an administrator who have worked with and observed Escalante rateda list of successful techniques according to the degree to which they explained Escalante's teaching success. Part 2 describes theresponses of senior high school students who had been Escalante's studentsfor 3 or 4 years to a similar questionnaire. Part 3 shows the results ofa similar rating process by several of Escalante's colleagues, which found a 7 percent level of agreement between students and colleagues. Part 4, the longest section, contains the taped transcription of an interview with Escalante designed to determine whether or not he agreed Yith his students' ratings of his teaching techniques and to ask whether his students had left out anything. Part 5 discusses the study's findings. Extensive appendixes contain information on the Jaime Escalante Mathematics and ScienceProgram, questions from the pilot test, questions from the other phasesof the study, student responses, abstracts of the paper, correspondence, and the study contract. Contains 29references. (a) U.S. DEPARTMENT "PERMISSION TO REPRODUCE Office of Educational Of EDUCATION THIS Research andImprovement MATERIAL NIBS BEENGRANTED BY EDUCATIONAL RESOURCES CENTER (ERIC)INFORMATION 14 do d This documenthas been reproduced ecteved from the as onginating a person or orgenization 0 Minor changes 4 have been made /tic reproduction Quality to Improve

Flotilla ca sew TO THE EDUCATIONAL ment do notor opinions slated inthis docu- ncessanty represent RESOURCES OERI positionor policy official INFORMATION Cr1TER(ERIC)

AN INSTRUCTIONAL GUIDE Concerning the Highly Successful Teaching & Motivating '2ractices of Jaime Escalante

for The Escalante Math Project at East Los Angeles College

Prepared by

Donald Kester, Ph.D. Consultant, Program Evaluation & Research Division of Educational Support Services Educational Program Evaluation

Los Angeles County Office of Education r

An Instructional Guide Concerning the Highly Successful Teaching and Motivating Practices of Jaime Escalante

Prepared for

The National Science Foundation Washington, D.C.

The ARCO Foundation Los Angeles, California

The Ford Motor Company and Foundation Dearborn, Michigan

_ and-

East Los Angeles College Monterey Park, California

Donald L. Kester, Ph.D. Consultant, Program Evaluation and Research Division of Educational Support Services Los Angeles County Office of Education Downey, California (310) 922-6415

March 1993

The Preface and Parts 1 and 2 of this paper were presented atthe annual conference of the American Evaluation Association (AEA) held in Washington,D.C. in November 1990 and at the California Educational ResearchAssociation (CERA) Conference held in San Diego in November 1990. The remainder of this paper waspresented at the Annual Conference of the American Evaluation Association held in Seattle,Washington in November 1992 and at the California Educational ResearchAssociation (CERA) Conference in San Francisco in November 1992. Table of Contents

Preface 1 Part 1 - The Pilot Test 10 Part 2 - Judgments by Escalante's Calculus Students 17 Part 3 - Judgments by Escalante's Colleagues 23 Part 4 - Interview with Jaime Escalante 28

Discussion 49 Caveats 66 Concerns About Validity 76

Conclusion 79 References 82 Appendix A Item 1 Project Description 85 Item 2 Project Staff 88 Item 3 Project Students 89 Appendix B Questions to Key Informants 90

Appendix C The Last Tier 92 Appendix D Questionnaire to Escalante's Calculus Students 96 Appendix E Responses of Calculus Students To One Question 101 Appendix F Responses of Calculus Students to Two Open-ended Questions 103

Appendix G Student Responses to Three Questions 105

Appendix H Abstract of Paper Presentations 106 Appendix I Dr. Michael Scriven's Letter 107

Appendix J Jaime Escalante's Contract 108 PREFACE

Introduction, Overview, and Acknowledgments

Introduction

In November 1988 East Los Angeles College(ELAC), acting on behalf of a private sector partnership, submitted a grant application to the National ScienceFoundation (NSF). The proposed three year project was entitled, "The JaimeEscalante Mathematics and Science Program." According to the abstract, the Escalante project wouldaddress:

"...the national need to increase the pool of applicants tomathematics based university programs and to increase the numberof well-trained mathematics instructors. (Additionally, the project would fund) .. .the expansion of the highly successful East Los Angeles College Advanced PlacementCalculus Program to include a second local high school, (and establish) ... asupporting mathematics program for three feeder junior highschools and their six feeder elementary schools." (ELAC, 1988, NSF Grant Application, p. 3.)

George Madrid of East Los Angeles College was to be theproject's principal investigator. As project director, George would be assisted by Paul Powersand Dr. Kevin Galvin, both identified as project counselors. These three constituted the entirenon-teaching professional project staff. The project envisioned the training of fifteen teachers bythe "nationally acclaimed master teacher, Jaime Escalante." (Ibid.) It was hoped that with the addedfunding requested, the successes of the East Los Angeles College Advanced Placement CalculusProgram could be "multiplied in many directions" to facilitate even greater gains by an even larger groupof inner-city minority students. (Ibid.)

Over the more than three year period (1989-1991+)the overall project cost would be approximately $1 million. Of that, East Los Angeles Collegewould contribute approximately 36 percent, the National Science Foundation approximately 37 percent,the ARCO Foundation approximately 15 percent, and the Ford Motor Companyapproximately 12 percent.

The NSF grant application contained thefollowing language regarding the preparationof a "Program Manual" or "Instructional Guide." prepared that documents the "... anInstructional Guide (Program Manual) will be body of techniques that make up theteaching and motivating methods of Jaime Escalante. .. The primary contributor of materialwill be Escalante . .. The product intended primarily for in-house instruction,will have value for the replication of the program in other communities. .." (ELAC, 1988, p. 21.) This document is hereby submitted tosatisfy the requirement to produce anInstructional Guide.

In addition, you are encouraged toread the article entitled, "The Jaime EscalanteMath Program" which first appeared in the Journalof Negro Education, volume 59, number 3(summer 1990). The authors were Jaime Escalante andJack Dirmann, associate director of theFoundation for Advancements in Science and Education(FASE). The article was copyrighted in 1990 andlater reprinted under separate cover (1990) by theNational Education Association (NEA).

In a real sense, the journal article beganand ended with Jaime Escalante. In hisinitial statement in the reprinted article, he wrote: "In recent years, I have beendeluged with questions from interestedteachers, community leaders, and parents about my successin teaching mathematics to poor minority children. I am not a theoretician; myexpertise is in the classroom and my first commitment is to my students.Nonetheless, I am willing to share my opinions on this subject in thehope that they might be helpful to otherprofessionals in the I am hopeful this article will provide answers.I have called field of education. of this upon my colleague, JackDirmann. ...to assist in the preparation manuscript." (Escalante and Dirmann,1990, p. 1.)

Since Mr. Dirmann's role was to assist,it seems clear that the primarycontributor to the journal article was Jaime Escalante. As will be seen,Mr. Escalante was the primary contributor tothis Instructional Guide as well.

Overview Jaime Escalante. It By way of contrast, this InstructionalGuide began elsewhere and ended with motivating, and began with questionnaires about researchfindings related to teaching, learning, asking respondentshis colleaguesand calculus studentsto identifythose findings which best explained his successful teaching andmotivating practices. It ended with avideotaped interview with Mr. Escalante in which heresponded to each relevant researchfinding identified by his calculus students. This Instructional Guide has severalmain parts:

Part 1 The Pilot Test

Part 2 Questionnaire responses from Mr. Escalante's calculus students.

Part 3 Questionnaire responses from Mr. Escalante's colleagues/ "key informants." Part 4 An edited transcription of a videotaped interview with Mr. Escalante.

Part 5 Discussion

Part 4, which consists of Mr. Escalante's transcribed remarks,is '26 pages long.This is considerably longer than Parts 2.or 3. Since he spoke last and longest, heshould be recognized as the primary contributor to this Instructional Guide as well as thejournal article. As the reader of Part 4 will notice, Mr. Escalante agreed that he does use theteaching and motivating strategies identified by his calculus students in Part 2 of this Guide. In theDiscussion part, one frame of reference will be suggested for summarizing the findings from this study.

It is one thing for an excellent teacher to describe what he believes andwhat he does; it is something different to begin with an identification of those attitudes and practicesof his which have most impressed others. The first approach (the journal article) concentrates onthe sender (the teacher), whereas the second (this guide) concentrates on the receivers (thestudents). While both sides of this transaction are significant in the teachinglearning interaction,it should be remembered that the active participants in this interaction are only two, the teacher andhis students; everyone else is either an observer or facilitator.

The approach taken in this guide combines Mr. Escalante'snotion that there are "common denominators" in the actions of "very effective teachers," and aprocedure in use in program evaluation referred to as "triangulation." First, Mr. Escalante's statement:

"...If we were to study the methods of a hundred veryeffective teachers, my guess is that we would find theirapproaches to be rather simple and direct, with many -common denominators....I believe we teachers should devote moretime identifying and implementing techniques that havewithstood the acid test of classroom performance. .." (Escalante and Dirmann, 1990, p. 6.)

For decades, educational researchers have sought toidentify those "common denominators" that have "withstood the acid test of classroom performance."In this Instructional Guide those common denominators are called "research findings," sinceresearch is required to identify those practices that have "withstood the acid test of classroomperformance." "Research findings" is also the term used in the booklet,WhatWQtka;licararlIlauarachingansaraming. in his recent book on qualitative evaluationand research methods, Michael Quinn Patton (1990) discussed "triangulation" as follows: One important way to strengthen astudy design is through triangulation, or the combination of methodologies in the study of the samephenomena or programs. This can mean using several kinds ofmethods or data, including using both quantitative and qualitative approaches. Denzin(1978b) has identified four basic types of triangulation: 1) data triangulationthe useof a variety of data sources in a study; 2) investigator triangulationthe use ofseveral different researchers or evaluators; 3) theory triangulationthe use ofmultiple perspectives to interpret a single set of data; and 4) methodologicaltriangulationthe use of multiple methods to study a single problem or program. The term triangulation is taken from landsurveying. Knowing a single landmark only locates you somewhere along a line in a directionfrom the landmark, whereas with two landmarks you can take bearings in twodirections and locate yourself at their intersection (Fielding and Fielding, 1986:23). The term triangulation also works metaphorically to call to mind the world's strongestgeometric shapethe triangle (e.g., the form used to construct geodesicdomes a la Buckminster Fuller).. . Triangulation is ideal. It can also be very expensive. Anevaluation's limited budget, short time frame, and political constraints willaffect the amount of triangulation that is practical. Certainly, one important strategyfor conducting evaluation research is to employ multiple methods, measures, researchers,and perspectivesbut to do so reasonably and practically. (Patton, 1990, p. 187)

Since this guide presents information from: 1)Mr. Escalante's colleagues (Part 1, 2) his calculus students (Part 2), and Mr. Escalante himself (Part 3), it presents"multiple perspectives" and uses the first basic type of triangulation listed above,data triangulation.(See Figure 1 below.) Furthermore, since different methods were used tocollect informationquestionnaires for Parts 1 and 2, and a structured interview for Part 3thisguide also uses multiple methods to obtain information. Figure 1 Data Source Triangulation

Jaime Escalante

His Colleague His Calculus Students

Mr. Escalante's colleagues and his calculus studentscompleted a lengthy questionnaire (see Appendix C). Then, in the videotaped interview, Mr. Escalanteresponded to the top 38 practices identified by his calculus students as more like him. By either questionnaire orinterview, the three sources of informationJaime, his colleagues,and calculus studentsresponded to the same items. Three sources responding to the same prompts give us ourdata triangulation.

The overall approach taken by this Instructional Guide can bedescribed by using a combination of logic and the language of mathematics, including set theoryand Venn diagrams. Consider the following:

Goal: To describe the contents of Set A

Where: Set A = {The successful teaching and motivating practices of Mr.Jaime Escalante }

To meet the goal, we first make some assumptions, then we reasonlogically.

Assumption # 1: Assume you can discover the contents of Set B

Where: Set B = (The successful teaching and motivating practicesidentified by prior research studies}

Assumption # 2: Assume there are common teaching and motivatingpracticesEscalante's "common denominators"in use by "very effectiveteachers"including Jaime Escalante himself.

"intersection" of Sets A and B (A n B) as shown 0 In the language of mathematics, we now have the in Figure

1 Figure 2 Intersection of Sets A and B

Where: Where: Set A = {The successful Set B = {The successful teaching and teaching and motivating practices motivating practices of Mr. Jaime identified by prior Escalante} research studies}

If Set B is known, and Set B intersects Set A, then by definition, the two setscontain some of the same elements, or practices. Furthermore, partof Set Athe common practicesthe shaded area in Figure 2 aboveis known. It is known because all of Set B is known. Atthis point, what is known and unknown is illustrated in Figure 3. e Figure 3 Set A After the Intersection With Set B

These practices These practiceswhich which are unique to were also contained in Jaime Escalante Set B ---are now known, are still unknown. since all of Set B is known.

Set A

Where:Set A ={ the successful teaching and motivating practices of Mr. Jaime Escalante}

Two major tasks now remain.Fortunately, both can be accomplished by interviewingMr. Escalante.

6 Final Tasks:

1. Verify, during an interview with Escalante, whetherthose practices identified by his calculus students as "common"the shaded area in Figure3are common; that is, they are practices he uses.

2.Identify, during an interview with Escalante, practices unique to him; thatis, identify the remainder of Set A.

Acknowledgments It is clear at once that the multi-year "Jaime Escalante MathematicsProject" could not have existed except for the efforts of this masterful teacherand the financial support provided by the National Science Foundation (NSF), the ARCO Foundation, FordMotor Company, and East Los Angeles College (ELAC).

Mr. Escalante's success in teaching advanced mathematics toinner-city, mostly Hispanic, students is well known. It has been described not only in a book,Escalante. the Best Teacher in America. 8 but also in a film "Stand and Deliver." His work has beenwell documented especially in the popular press. The project bears his name because it was built aroundhim. And, since the project cost more than $300,000 a year, outsidefunding was essential. Appreciation goes to Jaime for his leadership, to the funding agencies for their support, and tothe project director and his staff for their able management of the entire project. The projectitself was large, comprehensive, and complex. (See Appendix A for more detail on the projectand its many components.)

For their personal interest and support of the project manyindividuals at several agen- .3s need to be thanked. Appreciation goes to the following:

At the National Science Foundation Dr. Luther Williams, Director, Directorate for Science& Engineering; Dr. Charles Puglia, Division Director, TeacherPreparation & Enhancement; Dr. Joseph Stewart, Former Program Director,Teacher Preparation & Enhancement; and Dr. Russell Aiuto, Former Division Director, TeacherPreparation & Enhancement At the Ford Motor ard Foundation Frank V. J. Darin, Director, CorporateAffaire Office; and Leo J. Brennan, Jr., Executive Director, FordMotor Company Foundation

At the ARCO Foundation Fred Nelson, Program Officer; and Gloria De Necockea, Program Officer

At Eas Los Angeles College Dr. Omero Suarez, President, East Los AngelesCollege; Arthur Avila, Former President, East Los AngelesCollege; Ken Hunt, Former Dean of Academic Affairs, East LosAngeles College; George Madrid, Director, Escalante Math Project; Paul Powers, Counselor, Escalante Math Project; Kevin Galvin, Counselor, Escalante Math Project; and Maria Cabral, Yo li Alvarez, Marcella Nolasco, and AliceMaldonadoall program assistants to the Escalante Math Project

ALIQCosa-CalaCsaluZiounsawililatio Donald R. Green, President Coca-Cola Foundation,and Rudy Beserra, Senior Staff Representative forCorporate Affairs Coca-Cola, Mr. Green, and Mr. Beserra are thankedfor their support of a capital improvement feasibility study for the Escalante Math Project.

A number of people deserve to be thankedfor their valuable assistance in the development ofthis Instructional Guide. Most of them work eitherfor the Escalante Math Project or for the Los Angeles County Office of Education(LACOE). Those at the Escalante Math Projectwho should be recognized and thanked include: George Madrid,project director; Paul Powers, project counselor; Kevin Galvin, project counselor; AngeloVillavicencio, math teacher and key informant;Cathy Lum, assistant principal, Garfield HighSchool and key informant; and MatthewGalvin, video camera man who taped thehour-long interview of Jaime Escalante. (SeePar: 4.)

Very special thanks go to George Madrid,Paul Powers, and Kevin Galvin for manyenjoyable hours of discussion about teacher effectivenessin general and Jaime and his students inparticular. In addition, appreciation goes to Dr.Beverly Young, assistant professor, California State University at Fullerton, and Dr. Pat Wheeler,president, Educational Research, Evaluation, Assessment, and Policy Analysis Associatesand senior research associate to Dr. Michael Scriven. During the California Educational Research Conferencein San Francisco in 1992, both Pat and Beverly made worthwhile suggestions for improving the draft of thisGuide.

Thanks also to Dr. Daniel Snifflebeam, director of the Center forResearch on Educational Accountability and Teacher Evaluation (CREATE), Western MichiganUniversity, and Dr. Michael Scriven, adjunct professor, Evaluation Center, Western MichiganUniversity. Drs. Scriven and Stufflebearn came to my first Escalante paper presentation at the AmericanEvaluation Association Conference in Washington, D.C., in 1990, where we had a mostenjoyable discussion about Jaime and the keys to his successes. Thanks to Drs. Scriven andWheeler for flying down to Southern California; we had an enjoyable meeting and lunch withJaime and Kevin. Thanks to Dr. Scriven for his interest in and kind words about this InstructionalGuide. (See Appendix L)

Finally, those at the Los Angeles County Office of Education whoshould be recognized and thanked include: Dr. Fred Smith and Steve Yamarone for doing thestatistical analysis; Merlyn Madrigal for transcribing the videotape of the Escalante interview;Laurene Twineham and JoAnne Long for editing the transcription of the Escalanteinterview; and Merlyn Madrigal, Rachel Hoo, Lori Trent, and Connie Cortez for doing the wordprocessing necessary to produce this Instructional Guide. Administrators who supported this investigationinclude: Dr. Alice Healy- Sesno, consultant-in-charge, Evaluation, Research, andSupport Services; Dr. Nancy Krause, director, Educational Support Services; Dr. Gordon Footman,former director, Educational Support Services; Dr. Gilberto Anzaldua, assistant superinreadent,Educational Services; and Dr. Stuart E. Gothold, superintendent. Part 1 The Pilot Test

Seeking the Answer to the Question "Will This Approach Work?"

This Instructional Guide presents important perspectives on"...the body of techniques that make up the teaching and motivatingmethods of Jaime Escalante." (ELAC, 1988, p. 21.) Theapproach taken here was to: First, identify Set B, where SetB contained successful teaching and motivating methods identified by prior research studies; second,identify which of those methods were used by Escalante (identify the intersection of Set A andSet B); and finally, identify the remainder of Set A; that is, identify those unique methods that onlyEscalante uses.

But, would this research oriented approachwork? What Escalante does is obviously very successful, since his students are very successful, sothere is a Set A that contains the successful practices he uses.Is there also a Set B that contains successfulpractices identified by prior research? Does Set A intersect Set B? That is, are somepractices in Set B also in Set A? Does Escalante agree that he uses me pizetices on others reporthe does? Are there additional, unique practices he uses? These are the main questions thathad to be answered.

Part 1 reports answers to several of thesequestions. For purposes of this pilot test, Set B was identified as containing the 59 "Research Findings"(methods or practices) listed in the booklet entitled, What Works: Research About Teachingand Learning. (U.S. Department of Education, 1987.) Two colleagues of Escalante, a mathteacher in his department at Garfield High andhis assistant principal there were identified as"key informants." Angelo Villavicencio,the math teacher, had sat in Escalante's classes andobserved him teach for eight weeks. Angeloproudly states that, "For five years Jaime was mymaster teacher and mentor." CathyLum, the assistant principal, had for a number of years observedJaime teaching, both formally and informally.As knowledgeable informants, they agreed to readthrough the list of 59 "Research Findings" and rate each one on the degree to which itexplained Escalante's teaching success. Moreprecisely, they were given the followingquestion and response categories for eachfinding.1

1Key informants were asked several questions. Far more detail onthese questions, please see Appendix A.

10 Does this research finding to someextent explain the teaching success of Jaime Escalante? Yes, a great deal Yes, for the most part Somewhat Only a little No, not at all

Ideally, through their rating of each finding,Escalante's colleagues would scatter those findings across a continuum from thosethat very closely match what he does to those that do notmatch what he does at all. Fortunately, this is exactly whathappened.

Based on ratings by key informants, it waspossible to separate the 59 research findings into four groups. For convenience, these groupshave been identified as: "The first, second, third,and last tier." The fifteen findings in the first tier werejudged to be the best match. Both key informants answered, "Yes, a great deal" when asked thedegree to which each of these findings explain Escalante's success. This is shown in Table 1.

Table 1 Key Informant Judgment Calls On The Extent To Which Each of Fifty-NineResearch Findings Explain the Teaching Success of Jaime Escalante

Categories of No. of research explanation findings contained Where strength in each category displayed Actual judgment calls by key informants

The First Tier 15 Table 2 Both key informants answered, "Yes, a great deal."

The Second Tier 9 Table 3 One key informant answered, "Yes, a great deal," and the other answered, "Yes, for the most part."

The Third Tier 7 Table 4 Either both key informants answered, "Yes, for the most part," or one key informant answered,"Yes a great deal" and the other answered,"Somewhat"

The Last Tier 28 Table B-1 InAnswers did not exist or included the weaker Appendix B categories of "Only a little" or "No, not at all."

Note: All research findings were taken fromWhat Works: Research on Teaching andLearning. Second Edition, published by the United StatesDepartment of Education, 1987.

Research findings in the first three tiers areshown in the following three tables. The Top Fifteen Research Findings As ExplainingSuccess OfThe Jaime Teaching Esca !ante The First Tier Table 2 Identified by Key Informants 1. Developing"Many highly Talent successful individuals have 4. ladle:high"Teachers Expectations expectations who set to and all communicatetheir students 7. pehavioressential"Good Problemsclassroom for teachers management to deal with is particularintelligence.aboveonupon innate average hard activity ability" work but is and often(p. not 14). moreextraordinary dependent Accomplishment in a self-discipline than obtainsetfrom tow greater those expectations" students academic than (p. performance teachers35). who specificbutstudentsfrustrations.how such to suggestions whostudents cope chronically withThis also fromtheiralso benefit misbehave,conflictsteachershelps from them onand gain 2. kiala 5. Attaining Competence 8. Directinsights Instruction about their behavior" (p. 40). contributesandimportance"Belief the inimportance the to of greater valuepersonal of ofsuccess education hard responsibility, work,in school" itself the changesTeacherstakeskill,"As students ontheir can distinct whothinking determine acquire are knowledgeandalert how reasoning wellto these their and characteristics. demonstratestudents"Whenstudentsaccomplish teachers are learn expected a the more"particular explain steps (p. to exactly 41). neededacademiclearn, what and to task (p. 15). studentsproblembecoming are solvers" competentprogressing (p. 38). thinkers toward and 9. 3. caoperative"Studentslearn to Leaning in work cooperative toward learninga common teams self-esteem, goal, 6. Managingengaged"Howstrongly much Classroom in totime learning their students Time achievement. contributes are actively The Studylearn.influence"The Stalk waysTeachers strongly in whichcan often how children help much children study they takehelptheirlearning onemore classmates" another responsibility and comelearn, (p. 21). togain respectfor their and own like managementisamount determinedadministration"priorities of time skillsby available the (p. of instructional 39). the forteacher learning and set by the school develop better study skills" (p. 49). The Top Fifteen Research Findings Identified by Key As ExplainingSuccess The Of Teaching Jaime Escalante The First Tier Table 2 Informants 10. Homework, WNW. "Students achievement rises significantly 12. prior Knowleldge "When teachers introduce new subject (continued) 14. Character Education surrounding"Good character students is encouragedwith good adult by 51).andwhen studentu teachers conscientiouslyregularly assign homeworkdo it" (p. conceptsmatter,(p.grasp 55). theyits relationship haveneed previously to help to students learned"facts and occasionsexamplesclassrooms,knowgood character.how and for bytolearning and organizebuilding lessons and upon their topracticing foster natural schools, such Skillful educators 11. Homework Quay "Well-designed homework assignments 13. effective Schools "The most important characteristics of 15. Rigorous Curses examples""The stronger (p. 59). the emphasis on relatethoroughlycarefullyHomeworkstudents' directly learning is explainto most classwork beyond useful it, and thewhenand give classroom. extend teachersprompt prepare the assignment, expectationsonorderlyinstructionaleffective climate, for leadership, school student -wide achievement, a safeemphasis and basic schoolsskills, high are teacherstrong home,learnedschoolrigoroustheacademic subject studentssuch mainly the courses, as textbooks,matter, insciencelearn. school the Subjects andmore andthe rather themore math,advanced that thanmore high areare at Note:1987. MI Page research numbers findings in parenthesis were taken refer fromcompleted"comments to this and (p. !i3).criticism when the work is WhiasakOssarasalcuhing and Leaminn.publication. Second Edition, published by the progress"and continuous (p. 57). assessment of pupil kindmost of influenced courses by the number and United States Department of Education, BEST COPY AVAILABLE Nine More Research FindingsAs Explaining Identified The byTeaching Key Success Of Jaime The Second Tier Table 3 EscalanteInformants 1. Solving Word Problems 4. Assessment 7. Attendance onencouragesolving"Studentsproblem it, math will beforethem becomeproblems to they think more begin if through teachers adept working ata guide them through the "Frequentweaknessesmakersadministrators,helpsmonitoring students, identify of instudents' parents, strengths teachers,progress and and learning andand systematic policy absencesattendanceattention,encouragement"A school and can and staffclass-cutting" reduce andmonitors that personalized unexcusedprovides ( p.daily 63). 2. Illustrationssolvingregularthinking problems" and process, frequent (p. and 29). practice give them in 5. Schoolinstruction" Climate (p. 54). 8. Effective Principals students'photos"Well-chosen and learning" illustrations diagrams, (p. 34). can graphs,enhance discipline"achievement"Schoolsandimportance on that maintaining (p. encourage of58). scholastic academicorder success and focus on the "Successfulinstruction"environmentpolicies that principals( p.and create 64). support anestablish effectiveorderly 3. achievementlead"Students tutoring for bothother studentstudentsprlpg and can to improved academic 6. Disciplinebystudents'"Schools establishing, academic contribute communicating, achievement to their 9. Preparationlikelypositivestudents"Business to with workfind for work solidand attitudes keepbasic jobsareskills more than and leaders report that DepartmentNote: All research of Education, findings 1987. were Page taken numberstowardtutor, andcoursework" in to positive (p. 46). attitudes from What Works. Research on Teaching_and Learning. Second parenthesis refer to this publication. disciplineand enforcing policies" fair and(p. 61).consistent Edition published by thealone"students United ( p.States with81). vocational skills 2 The Bottom Seven Research Findings As Explaining The Teaching Success The Third Tier Table 4 Identified by Key Informants Of Jaime Escalante 1 Counting 4. yarning Mathematics 7. Questioning arithmeticknowledge."A good isway to buildto teach on theirchildren informal simple This is why learning to theymathematics"Childrenlessons" use physical (p.in more 27).early effectivelyobjects grades in learnwhen their studentsteachers"Studentand evaluate to askachievement apply, questions information analyze, thatrises synthesize, in additionrequire when to 2. sciencebasiscount11). foreveryday Experiments early arithmetic objects is lessons"an effective (p. 5. Teacher Feedback simply recalling facts" ( p. 48). 17. arewitness"Children able to 'science do learn experiments, science in action" best so(p. when24). they they can wellsuggestions,including"Constructive as develop deserved helpsfeedback positive praisestudents from self-esteem" and teachers,learn, specific as 3. Estimating 6. hiontaizalian(p."Memorizing 45). can help students absorb Thistheproblems,find"Although helpful skill can goodstudents skill be math oftaught" estimatingneed students (p. to 25).learn alsoanswers. how learn to exact answers to arithmetic whichandthought retain understanding are the based" factual (p. information 47).and critical on Note:Education, All research 1987. fodings were taken from I '1 I I I' II I ' cry .1 , published by the United States Department of The pilot test showed that theapproach taken here would work. Set A certainly exists; and SetB can be thoughtof as containing those teaching and motivating practicesthat are found in the booklet, ahatasula....RemsuchAbolatachiligaing.Furthermore, Set A and Set B do intersect; that is, some practices listed in WhatWorks are practices used by Escalante. (See Figure 4.)

Figure 4 Intersection of Sets A and B

Last Tier

First Tier

Where: Set A = {The successful Where: Set B = (The successful teaching teaching and motivating and motivating practices practices of Mr. Jaime identified in the booklet, Escalante } What Works}

The 15 research findings in the first tier (Table2) were clearly judged to be "common"; that is,they are contained in both SetB and Set A.

The 28 research findings in the last tier (Table B-1in Appendix B) were clearly judged to be inSet B but not in Set A. The pilot test showedthat Mr. Escalante was right when he said it waspossible teachers" that have to identify "commondenominators"practices in use by"very effective "withstood the acid test of classroom performance."(Escalante and Dirmann, 1990, p. 6.)

16 94 Part 2 Judgments by Escalante's Calculus Students

As noted earlier, the primary interaction of interest isthe teachinglearning interaction. There are only two categories of participants in this interaction;the teacher, Jaime, and his students, everyone else is either an observer or facilitator. Whilethe judgments of observers can be very helpful, the judgments of the teacher and his students are essential.Angelo Villavicencio had observed Escalante for eight consecutive weeks and, while no otherobserver has been able to duplicate this, some of Escalante's students have beenwith him for several years.

Escalante's calculus students were chosen as the primary sourceof information about his teaching and motivating practices for several reasons. First, as studentsthey were direct participants in the teachinglearning interaction. Second, they had Mr. Escalante astheir math teacher for three or four years, so they knew him better than other studentsdid. Third, they tended to be high school seniors who were planning to transition to college. They were,therefore, older and hopefully better able to be objective about their experiences with him.

The same approach that guided the data gathering fromEscalante's colleagues (Part 1) was used to guide the data gathering from his calculus students exceptthat this time, Set B, the set containing the successful teaching and motivating practices identifiedby prior research, was expanded.

In Part 1, Set B contained 59 research findings taken fromWhat Works: Research on Teaching and Lamming. (U.S. Department of Education, 1987.) In Part 2, Set Bcontained statements taken from the following three sources:

1) What Works: Research About Teaching and Learning(2nd ed.) 1987 published by the U.S. Department of Education

2) ItsaiyatimuWhakEricsaarraSsullsLict 1982 publishedby the National Education Association

3) :Thtlaimalsolarligalaa2curam 1990 published bythe National Education Association

1 17 t 95 In all, 75 statements about Mr. Escalanteand his actions were created and presented to his calculus students by way of a questionnaire.(See Appendix C for a copy of the questionnaire.)Each statement had been derivedfrom one or more of the three sources mentioned above. His sruuents were asked to rate each statement; e.g.,"Mr. Escalante is often funny or humorous," by assigning a number from minus nine to plus nine (-9 to +9) to each statement.Minus nine (-9) meant the student "very strongly disagreed" with the statement,while a plus nine (+9) meant that he "very strongly agreed" with the statement.

Escalante's calculus students were able to scatter the75 statements across a continuum. Interestingly, the statement, "Mr. Escalante is oftenfunny or humorous," rose to the top of the list with an average rating of 8.362 (range -9 to +9). Ofall statements, this one was judged to be the one most like him. At the otherend of the list was the statement, "Mr. Escalante encourages me to get involved in extra curricularactivities to round out my education." This onehad an average rating on only 1.674 (range -9 to +9) and wasjudged to be the one most unlike him. Please see Table 5 which follows. Rank Ordering of Selected Statements Regarding and His Teaching by His Calculus Students TABLE 5 Jaime Escalante OrderRank 1 CalculusMean Students Rating by n=47 Original QuestionnaireStatement Number Statement NEA, 1990, p.7) 243 8.0878.3627.9788.022 65641014 7 believesis oftenexpectsputs academicsfunny my me first toor achieveworkhumorouspriority first hard (USDOE, andis to(USDOE,(Evaluator's do learn well 1987, (USDOE, in 1987, mathp.classroom 58; pp. (USDOE, NEA,1987, 14, observations p. 58; notes; 15; NEA,1990, 1990, p. p. 8) 1987, pp. 35, 58; NEA, 1986, p. 22; NEA, 8) NEA, 1990, p. 8) 657 7.8917.9577.766 75 3 hasis helped enthusiastic me understand (NEA, 1986, that employersp. 20) will wantwriting,1990, me p. to and9) have problem a solid solving (USDOE, 1987, p. 81) preparation in math, reading, 9710 7.5747.7617.766 6811 4 isexpects energetican excellent me to(NEA, attend mathematician 1990, class, p. come 8) (NEA, to class 1990, on pp.time,pp. 7, 35, and8, 59;10) meet NEA, 1986, p. 22; NEA, 1990, p. 8) the assignment deadlines (USDOE, 1987, 1112 7.511 43 9 expectsis cheerful that I (NEA,can and 1986, will learn,p. 20) a lot of mathpp. 4, 9) . (USDOE, 1987, p. 35; NEA, 1986, p. 20; NEA, 1990, 141315 7.4357.4897.1067.234 674227 callshasexpects helped attention me me to betosee diagrams,honest, that education coeaeous, graphs, is importantphotosand to showorpp. illustrations(USDOE, respect1, 11) 1987, that p.not only for others (USDOE, 1987, p. 59; NEA, 1990, 15; NEA, 1990, p. 9) relate to the lesson but also 1617 7.0227.000 4653 encourageshas taught me me to rules try harder and principles by reminding and the me conditionshelp thatbow mepeople well learn under we and do which remember(USDOE, they apply (USDOE,1987, so pp. 43,1987, 57) p. 34; NEA, 1990, p. 4) beyond our school are paying attention to I can solve math 1719 6.9797.000 71 6 hasis helped friendly me toward understand me (NEA, that I learn1986, more p. 20; in NEA,1990,problems rigorous,(USDOE, (USDOE,tough 1987, courses p. 1987, 75; than NEA, p. 38)in courses1990, pp. 3, 4) pp. 9, 10) that are easier (continued) Table 5 Rank Calculus StudentsMean Rating by Original QuestionnaireStatement Number Statement Order 212022 n=476.8916.9136.745 621718 giveshelpshas meencouraged me a lot enjoy of math publicmath problems (NEA, recognition 1990, to for p. 7)( USDOE, 1987, p. 57) (USDOE, 1987, p. 39; NEA, 1990,do (USDOE,p. 8) 1987,students p. 14; who NEA, succeed 1990, and p. promoted a sense 7) of school pride 23262524 6.7396.6386.6606.723 4745211213 capturesrequiresbelieveshelpshas helped meand thatin see holds meme fastermyself set(USDOE, my higher learners attentionas a goals "winner"1987, put forforth p. 35; effort too; myself(USDOE, in life (NEA, 1987, 1990,p. 35; p.NEA, 9) 1986,NEA, p. 15; 1986, NEA, p. 22; NEA, 1990, p. 9) he won't let them just "coast" (USDOE, 1990, p. 9) 1987, pp. 14, N 272928 6.5326.5536.574 2516 expectshasgives helped me me the me to help spendunderstand 1 need a lot when ofthat time I Ican get on become37, 78)1990, pp. 5, 9) "stuck" math(USDOE, (USDOE, 1987, 1987, p. 45; pp. NEA, 15, 75)1990, pp. qualified for any job I want (USDOE, 1987, p. 8, 9) 35; NEA, 0 313032 6.4266.4576.511 385222 hastakes helped us through me learn the stepshow toneeded think tothrough solve achallenges1987, p. 41) I face and explore alternative strategies in mathproblem (USDOE,word problem and 1987, explains beforep. 35; the NEA,I beginpurpose 1990, working of p.each on step before I start to work(USDOE, 1987, p. 29) it; to analyze the 9)(USDOE, 3335 6.2986.340 37203219 hasunderstandshas helped helpedtaught me meme theset tobecome worldhigher estimate Imore goalswill answers face interestedfor myselfafter to high in know when an answer is "in the ballpark" math problems so that I can reject unreasonablemath answers (NEA, 1990,school p. 7) (NEA, 1990, p. 9) (USDOE, 1987, p. 25) and 38373539 6.1746.2616.2776.298 616615 helpshelpsexpects me me plan and see andrewards bow strive new my forinformation academic excellence successrelates top. 55) (NEA, 1986, p. 18; NEA, 1990,(USDOE, p. 6) 1987, pp. old35, information58; NEA, 1986, we have p. 22) already covered . (USDOE, 1987, 414042 6.0656.0856.043 7423 8 giveswouldis considerate me much math rather ofproblems me I not(NEA, takeI can 1986, a dopart-time if p. I paid job attention(USDOE,( USDOE, 1987, 1987,_ p. 80) pp. 54, 55; NEA, 20; NEA, 1990, pp. 9, 10) 1990, pp. 7, 8) that would require 15 hours or more per week during his lectures and did the assignments of my time (continued) Table 5 OrderRank 43 Calculus StudentsMean Rating by n=476.000 Original QuestionnaireStatement Number 26 hasStatement helped me learn how to work hard and take1990, p. 8) responsibility for myself (USDOE, 1987, p. 14; school NEA, 4345 6.0005.979 726941 hasenforcesrefers helped back mediscipline to see experiences the policiesadvantage I haveconsistently of alreadyadvancing andhad(USDOE,55; NEA, 1987, 1990, p. pp.78; 7,NEA, 8) 1990, p. 4) fairlywhen (USDOE, he introducesin 1987, math p.at new 61)a faster concepts pace by(USDOE, attending summer 1987, pp. 54, 48474649 5.8945.9155.9785.851 3936 5 hasis "warm"lets guided me know emotionallyme through quickly thetoward why thinking I gotme a(NEA, processesmath (USDOE,correctly (USDOE, 1987, p. 45;1987, NEA, p. 29; 1990, NEA, p. 8) problem wrong and what I should1986, have p. 20; done NEA, and 1990,1990, p. pp. 9) 7, I8) need to understand in order to work word problemswhy t.i 5150 5.8485.745 2959 giveshas mehelped homework me understand that is useful, that I asis aan learnerand need1986, counts to p. toward7; NEA, my 1990, grade pp. (USDOE, 12, 13) important part of classroom instruction,1987, p. is53) evaluated with especiallybe difficult active lifenot situationspassive (USDOE, ((USDOE, 1987, p. 39; NEA, by him 535254 5.6745.5745.596 48355130 letsworkssequenceshas me helpedpersonally know what mequickly seewith we thatwhethercover students I can in Iclass control todid help aso math themmy own cope1987, p. 40; NEA, 1990, p. 9) that my knowledge builds on itself and I am problem correctly or not (USDOE,destiny (NEA, 1987, 1986, p. 45) p. 18; NEA, 1990, pp. 5, 9.) ready for the next 565557 5.5565.4785.522 5456 praiseshas helped successful me memorize aspects of math my work facts andby (USDOE,stepfeedback (USDOE, 1987, from 1987, p.him 45; pp.when NEA, 20, I 39; get1990, correct p. 10) answers NEA, 1990,teaching pp. 7, highly 8) structured and givescarefully me detailedsequenced recommendations lessons for how I can (USDOE, 1987, p. 47) improve with 605958 5.3405.4685.130 406334 refershashas given backpromoted me to frequentmy agreement prior practice knowledge by the in doingprincipal, when wordsubjects1990, pp. and 7, 8)topics to be taught fUSDOE, introducingteachers, new concepts students, (USDOE, and parents 1987, on pp. the 54, goals, problems55; methods,NEA, (USDOE,1987, 1987, p. 57) p. 29; NEA, 1990, p. 8) (continued) Table 5 OrderRank 61 Calculus StudentsMean Rating by (n=47) 5.000 Original QuestionnaireStatement Number 49 monitorsStatement each student's progress so that all ofwe us arelearn actively (USDOE, engaged 1987, in p. learning 37; NEA, no matter1990, p.how 10) fast 65646362 4.7664.8304.8484.957 446057 2 rewardspresentsmonitorshas helped slowermath my me progress lessonsachieve learners clearly frequentlymore for their by (NEA, asking progress and 1986, systematically both and p. factual (USDOE,effort20) and(USDOE, (USDOE, more1987, complex, 1987, p.1987, 48) p. p. 37)thought-provoking 54) questions 69686766 4.4474.5744.6384.652 282458 1 managesishas well helped organized our me in-class developplan (NEA, further time better 1986, efficientlyinto study p.the 20; skillsfuture soNEA, that (USDOE, than 1990,disruptions I ever pp. 1987, have 7, and8) p. before 49)wasted (NEA, time 1990,are kept pp. to 5, a 9) minimum Ni..) 7071 3.8914.435 7050 worksmanages with classroom other math time teachers well by at keeping Garfield wasted achievementHigh(USDOE,1987, to time develop p. and 1987,(USDOE,39) misbehavior math p. 39;related 1987, NEA, to p.goals a 67)1990, minimum that pp. emphasize 7, 8) student (USDOE, 737472 2.8723.2343.600 333155 hasunderstandsprovides tried meto get whataccess my my parentsto lifea math at to home tutorbecome iswhose like involved (NEA, assistance and17; 1990, NEA,supportive has p. helped 12) 1990, ofme pp. my 10, school 11) work (USDOE, 1987, p. 46.) (USDOE, 1987, p. Association,secondNote: Statements Edake, 1986; published were and 75derived 3) by lbrlaimEssalatualdiuMagam, the from United research States findings Department which publishedofwere Education, taken by from the1987; the National following2) Motivation: Education three mainWbatesearch Association, sources: says1) What1990. to the Works. Teacher, Research published on Teaching by the National and Learning, Education 1.674 73 encourages me to get involved in extracurricularp. 79) activities to round out my education (USDOE, 1987, Part 3 Judgments by Esealante's Colleagues

In order for data triangulation to exist, the threedata sources must supply information on the same thing. The primary data collection instrument is the oneshown in Appendix C. This questionnaire was completed by Mr. Escalante'scalculus students and the results were reported in Part 2. To meet the requirements of data triangulation,both Mr. Escalante and his colleagues needed to respond to all or part of that questionnaire.

Mr. Escalante's colleagues were asked to completethe same questionnaire (Appendix C) that his calculus students had completed.His colleagues ranked the seventy-five statements abit differently. The ranking by his colleagues are shown in Table6 below. So that a comparison can be made of how both groups responded, statementsranked as more like Mr. Escalante by his calculus students are identified in this table by the print thatis both bold and italicized (see Table 6).

As can be seen in the table, there were only ten statements outof the top thirty-eight in this table that were identified by Escalante's colleaguesbut not by his calculus students (only ten were notprinted in bold and italics.) Put another way, his colleaguesidentified twenty-eight of the thirty-eight statements identified as more like him byhis calculus students. This fraction (28 + 38) equals74 percent, so there is a 74 percent levelof agreement between the two data sources (colleaguesand students).

23 Rank Ordering of Selected and His Teaching by StatementsTABLE Regarding 6 Jaime Escalante Key Informants Rank Ratings by Key Informants . Math Assistant Original Questionnaire Statement Order 1 n=29.09.0 Teacher 9 Principal 99 Statement Number 321 is presentsisenthusiastic well organized math lessons (NEA, (NEA, clearly 1986, 1986, (NEA, p.p. 20; NEA, 1986, p. 20) 20) 1990, pp. 7, 8) 1 9 . 90 . 0 99 99 162 2 4 givesis expectsenergetic me the mehelp (NEA, to I spendneed 1990, when a p.lot 8)of 1990, pp. 8, 9) time on math (USDOE,I get "stuck" 1987, (USDOE,pp. 1987, p. I need to understand in order to work word 15,45; 75)NEA, 1 9 . 9.00 9 9 4339 expectshas guided thatme through 1 can the and thinking will learn processes aNEA,problems 1986, correctly p. 20; (USDOE, NEA, 1987,1990, p. pp.29; lot of math (USDOE, 1987,NBA. p. 35; 4, 9) 1990, pp. 7, 8) A 1 9 . 0 9 99 4645 requireshas taught that mefaster rules learners and principles put forthapply"coast" so I(USDOE, can solve 1987, math pp.problems 14, 37, and the conditions under whicheffort too; he won't let them78) just(USDOE, 1987, p. 38) they 11 9 . 9.00 999 99 475348 sequencescapturesencourages whatand weholds me cover to my tryin class attentionharder so next step (USDOE, 1987, pp. 20, by remindingthat my knowledgeme that people builds on beyond 39;itself NEA, and our 1990,(USDOE, pp. 7, 8) 1987, p. 39; NEA, 1990, p. 8) I am ready for the 1 9.0 9 9 55 provides me access to a math tutor whose assistance5school 7 ) are paying attention to how (USDOE, 1987, p. 49) well we do (USDOE, 1987, pp. 43,has helped me (USDOE, 1987, p. 46.) 1 99.0 . 0 999 999 625958 hasgives helped encouraged me homework me develop public that better is recognitionuseful, study is skills an by him and counts toward my grade (USDOE, 1987, p. 57) important(USDOE, part of 1987,for classroom students p. 53) instruction, who succeed is and promoted a evaluated 11 9 . 9.00 9 99 6665 , expectsbelieves and my rewards first priority my academic is to learn success8)senseNEA, of 1986, school p. pride 22) (USDOE, 1987, p. 58; NEA, 1990, p. (USDOE, 1987, pp. 35, 58; (continued) Table 6 Rank Ratings by Key Informants Math Assistant Original Questionnaire Order 1 (n=2)map 9 . 0 Teacher 9 Principal 9 Statement Number 67 Statementexpects me to be honest, courteous,(USDOE, and to show 1987, respect p. 59; NEA, 1990, pp. 7, 11) and meet the for others 1 9.0 9 9 99 68 enforcesexpects discipline me to attend policies class, consistently come and toassignment classfairlyNEA, (USDOE,on 1990, time, deadlines p.1987, 8) p. 61)(USDOE, 1987, pp. 35, 59; NEA, 1986, p. 22; 1 99.0 . 0 99 99 756972 has helped helped me mesee theunderstand advantage ofthat advancing employersschool in math (USDOE, will at awant faster 1987, me pace p. to 78;by NEA, 1990, p. 4) haveattending a solid summer 25 8.58 . 5 9 8 67 expectsis friendly me toward to achieve me (NEA, and do 1986, wellpreparation inp.1987, math20; NEA, p.(USDOE, 81) in 1990, math, pp. reading, writing, and problem solving 1987, pp. 35, 58; 9, 10) (USDOE, t..,t.) 225 5 8 . 8.55 99 8 98 is consideratecheerful (NEA,of me (NEA, 1986, 1986, p. 20) p. 20;NEA, 1986, p. 22; NEA, 1990, p. 9) NEA, 1990, pp. 9, 10) 2525 8 . 88.55 . 5 99 88 101211 is believesisoften an excellentfunny in meor, mathematicianhumorous(USDOE, 1987,(Evaluator's (NEA, p.NEA, 35; 1990, classroomNEA, 1990, pp. 1986, p.7) p. 22; NEA, 1990, p. 7, 8, observations notes;10) 252S 8 . 85 . 5 9 88 1314 expectshelps me tosee work myself hard as (USDOE, a "winner" 1987,9) 15;(USDOE, pp.NEA, 14, 1990,1987, 15; p. 9)35; NM, 1986, p. NEA, 1990, p. 8) 1990, p. 25 8.58 . 5 99 8 1815 helpsha: helpedme enjoyplan me and math become strive (NEA, morefor 1990,excellence interested p.6) 7) (NEA, in math 1986, (NEA, p. 18;1990, NEA, p. 7) I 25225 5 8.588.5 . 5 9 88 20192129 hashas helped helped me me understand setset higherhigher that goals goalsI as a learner forforNEA, myself myself need 1990, to in inbe math lifeactivep. 9)(NEA, (USDOE, not passive 1990, 1987, p. 9) p. (USDOE, 1987, p. 35; 225 52 5 8.58.5 9 88 3035 letshas helpedme know me quickly see that whether [ can control 1 did a my math own9.)39; problem destinyNEA, correctly1986, (NBA, p. 1986, or7; notNEA, p. (USDOE, 18; 1990, NEA, pp. 12, 13) 1987, p. 45)1990, pp. 5, Table 6 Rank Ratings by Key Informants Math Assistant Original Questionnaire (continued) Order 2S (n..-2)Mean 8.5 Teacher 9 Principal 8 Statement Number 37 hasStatementhas taught given meme frequent to estimate practice answers in doing toword(USDOE,unreasonable math problems problems 1987, (USDOE, answers sop. 25) and know when an answer is "in the 1987, p. 29; NEA, 1990,that 1 can reject ballpark" 25 8.58.5 99 88 424140 callsrefers backattention to experiences to diagrams, I have already graphs, had whenrelateP.photos 8)1987, he tointroduces pp.or the illustrations54, lesson 55; new NEA, conceptsbut 1990, also pp. help 7, 8)me learn and remember (USDOE, that not only (USDOE, 25 8.5 99 8 5150 managesworks classroompersonally timewith wellstudents by keeping to help wastedthem(USDOE,1987, cope withp. 1987, 34; especially NEA,p. 39) difficult1990, p. 4) time and misbehavior to a minimum life situations 25 8.58.5 99 8 52 57 takeshas helpedus through me achieve the stepsmore by needed asking both topurpose((USDOE, solve factual a and problem of1987, moreeach p. complex, 40; stepand NEA, (USDOE, 1990, p. 1987,9) p. 41) thought-provokingexplains the 252 5 8.5 9 8 6163 hashelps promoted me see how agreement new information by the principal, relates teachers,to(USDOE,questions oldmethods, information students, (USDOE,1987, subjects p. weand 55) 1987, andhave parents topics alreadyp. 48)on to the be taught (USDOE, 1987, p. 57) covered goals, 252S 8.58.S8.5 9 88 647174 putshaswould academics helped much me rather first understand I (USDOE,not take a part-timethat 1987, I learn jobp.in 58; thatcoursesmore NEA,would in rigo;requirethat are 15 easierhours or (USDOE, more per 1987, p. 75; NEA, 1990, p. ns, tough courses than 1990,8) pp. week of3, 4) 55255 5 8.08.0 79 97 1723 givesgives me me a lotmath of problems math problems I can do if Ito paid dop. attentionassignmentsmy (VSDOE, time (USDOE,during (USDOE,1987, his 1987,lectures p. 1987, 14; p. and80) pp. did 54, the 55;7) NEA, 1990, pp. 7, 8) NEA, 1990, 555 5 8.0 8 88 362824 letsmanageshas helpedme know our me in-class quickly plan further timewhy efficientlyIint got ) thea math future so problem that than disruptions(USDOE,minimum I wrongever have and(USDOE,1987, before what p. 45;I 1987,should NEA, p. have 1990,39; doneNEA, p. 8)and 1990, pp. 7, 8) and wasted time3i are kept to a (NEA, 1990, pp. 5, 9) why (continued) Table 6 Rank Mean Ratings by Key Informants Teacher Math PrincipalAssistant Original QuestionnaireStatement Number Statement Order 555 5 (n=2) 8 . 08.0 88 88 38 54 haspraises helped successful me leans aspects how of myto workthink andstrategiesworking beforeon it; to 1 analyze start to workthe challenges (USDOE, throughgives me a detailedword problem recommendations before forI begin how 10) 1 face and explore alternative1987, p. 29) I can S5 5 8.08.0 78 89 564460 hasrewardsmonitors helped meslower my memorize progress learners mathfrequently for factstheir by progressand systematically andlessonsimprove with (USDOE, feedback 1987, from p. him 45; whenNEA, I 1990,get correct p. answers teaching highly structured and carefully sequenced effort (USDOE, 1987, p. 37) (USDOE, 1987, p. 54) (USDOE, 1987, p. 47) 6 56564 77.07.5 . 7.00 6976 885 2 526 5 hashasis "warm"helped helped emotionallyme learn understand how toward to work thatme hard (NEA, I can and (USDOE,take 1987, p. 35; NEA, 1990, pp. 1986, p. 20; NEA, 1990, p.become 9) qualified for anyresponsibility job 1 want for myself (USDOE, 1987, p. 5, 9) --) 656 569 4.07.0 75 73 7334 encouragesrefers back tome my to getprior involved knowledge in when introducing55;(USDOE,14; NEA, NEA, 1990,new 1987,1990, pp. p.p 7, 8)79) 8) extracurricular activities to round out my education concepts (USDOE, 1987, pp. 54, N/A Blank 9 32 72 31 hasunderstands helped me what seethe my world thatlife ateducation homeI will isface like is (NEA,after1990, p. 9) important (USDOE, 1987,high1990, p. 15; schoolp. 12)NEA, (NEA, 1990, p. 9) (USDOE, Blank 9 4933 monitorshasworks tried towitheach get otherstudent's my parents math progress teachers to become so at that Garfield involved allhow1987, fast p. 17;we NEA,learn (USDOE, 1990, pp. 1987,10, 11) p. 37; Highof us areto develop actively math engaged related in learninggoalsNEA, that no emphasize 1990,matterand supportive p. 10) of my school work Note: Statements were derived from 9 research findings which were taken from 5 70 the following three main sources: 1) student achievement (USDOE, 1987, p. 0 I I I I I .1 I II Edition,stuchnts1986; published to and be more3) by Ibmigiinabeglantradallmgvuu the like United him. States Department of Education, 1987; 2) published by the National Education Association, rtrpT (turn 11,10,, Motivation: What Research says to the Teacher, 1990. Statements in bold and italicized are published by the National Education Association, those identified by his calculus S

Part 4 Interview with Jaime Escalante

The primary purposes of the interview were twofold.First, to see if Mr. Escalante agreed or disagreed with the statements about him which his calculus students hadidentified as most like him. For example, did he agree or disagree that he was "often funny or humorous?"(He did.) Second, to identify any teaching and motivating practices whichhad been left out. (See list of "Final Tasks" following Figure 3.) Were there other major techniques or methods or practices he usedthat had not been identified and discussed? (He identifiedseveral.)

It was during the summer session of 1991 and Jaime had justfinished teaching his trig/math analysis class which met in a temporary building on the East Los AngelesCollege campus. He said he would rather do the interview in a room at the Escalante MathProject office. Mr. Escalante, Matthew Galvin, and I walked across campus with Mat carrying hisvideo camera.

The project director, George Madrid, said, "Here, use my office." Matadjusted his equipment and the interview began. We talked about "GANAS" (strong desire), thedemographics of his students, the first thirty-eight statements identified by his calculus students as morelike him, and the practices he uses which we had not yet identified. Many of those additionalpractices revolved around enlisting the support of the parents. (See Appendix J for Jaime's contractwhich requires the parents' signature.) As the interviewer, I thoroughly enjoyed myself.To me, this exceptional teacher is captivating and demanding as well as warm and caringtoward his students; he is also funny and inspirational. He seemed to enjoy our time together too; at leasthe stayed and talked for over an hour.

Here is what he had to say. Here is the edited transcription ofthat interview.

28 c# .ESCALANTE INTERVIEW

Dr. Kester: Hello. My name is Don Kester. I am a consultant in program evaluation at the Los Angeles County Office of Education.I am the external program evaluator for the Jaime Escalante Math Project. This project is fundedby the National Science Foundation (NSF) and ARCO. It has been in operationfor the last three years, 1989, 1990, and 1991, and while certainactivities will continue through June, 1992, this summer--the summer of1991--is the last summer of the project, and the last summerduring which Mr. Escalante will be acting as a math teacher. This fall he leaves southernCalifornia to go to Sacramento to teach math there. A grant application isbeing prepared to support his efforts there; and thatproject may also be called the "Jaime Escalante Math Project." In the future, he plans to act as aconsultant to this southern California project, which we probably should call,the "Original" Jaime Escalante Math Project.

We are here to interview Mr. Escalante aboutthe development of an "instructional manual." This manual was promised in theoriginal 1988 grant application to NSF. The manual was to describethe "very successful teaching and motivating methods" he uses.

Now before we begin the interview, I need to mentionseveral references that may come up in the discussion.These references are:

1.The bOoklet entitled, "WHAT WORKS:Research About Teaching And Learning", Second Edition, published bythe United States Department of Education (USDOE),

2.The booklet entitled, "MOTIVATION: WhatResearch Says To The Teacher" published by the NationalEducation Association (NEA),

3.The journal article entitled, "The JaimeEscalante Math Program" by Mr. Escalante and Jack Dirmann, reprintedby NEA, and

29 4.) The book entitled, ESCALANTEThe Best Teacher in America, by Jay Matthews.

To provide a basic, theoretical framework that wouldguide the investigation to identify and describe histeaching and motivating methods, research findings from the first two references were relied uponheavily. Research findings were turned into statements about Mr.Escalante and his teaching; e.g., "Mr. Escalante expects me toachieve and do well in math." This particular statement was developed from a page on"Teacher Expectations" in WHAT WORKS (p. 35). On a questionnaire,Mr. Escalante's calculus students were asked to rate each of seventy-fiveresearch-based statements on a scale from minusnine (Very Strongly Disagree) to plus nine(Very Strongly Agree). Using the ratings given,the statements were then rank- ordered from the one that was most likehim, "...is often funny or humorous", to the one least like him, "...encourages me to getinvolved in extracurricular activities...". For this interview, wewill ask Mr. Escalante to react to the first thirty-eight statementsthat were rated as more like him.

Dr. Kester: Let's go over now to interview Mr. Escalante,the man who has been called, "The Best Teacher in America." (The titleof the best selling book about you.) Mr. Escalante, it must be a great sourceof pride and satisfaction to you to know that youhave changed hundreds of lives of students overthe years.

Mr. Escalante: At Garfield High School we feel really greatwhen we see these kids going to the best colleges and universities of thenation. I have kids in USC, UCLA, MITyou name it. The only thing I don'tlike is the title, "Escalante, the Best Teacher in America." I knowthere are many other great teachers in America.

Dr. Kester: You have received praise over the yearsfor the wonderful things you've done and in my view you deserve all thepraise you've received and more. I want to take this opportunity tothank you for letting me into yourclass to observe, because I thoroughly enjoyedthat. In fact, I not only enjoyed itI was inspired by what I sawand heard.

30 Mr. Escalante: Thank you, it was fun.

Dr. Kester: Now as we go through each statement that the students in your calculusclass said was like you, please let me know if you think the statementis true or not, give some examples of what youdo that illustrate the statement, and if it isn't really obvious, please describe how thisattribute of yours or this teaching style of yours helps the students learn.

Mr. Escalante: Doing mathematics is fun.That's what I'm trying to put across to the students. Another key factor is keeping themfor three consecutive years so you don't break the continuity.That's when kids come to realize that math is fun.

Dr. Kester: Let's get something straight right at the outset, too.Your students are not gifted students, they're not students withhigh test scores, they're not students with high grade point averages. These aretypical students from this area of East Los Angeles.

Mr. Escalante: It is true we have a homogeneous class.Most of the kids are Mexican- Americans. Also it's true the kids are not motivated todo any math and they don't like to be involved in academic classes.One of my first functions was to motivate them to be in my programand eventually in any college they choose.

Dr. Kester: The research that we've done shows that 99 percentof the students are from an ethnic minority groupand that when we looked closely at incomelevel, we found that the medianincome for a typical (median) family of five was about $16,500 a year. We also foundthat 57 percent of fathers had not finished high school and 21 percent hadfinished high school only. So this is the population with which you're working.

graduated from high school. And so, Mr. Escalante: Yes, a majority of the parents have not in many cases they're not really happyabout their kids going on to college. That's one of .1.1e things we have to face.

31 4 7 Dr. Kester: Given this student population and the fact that you're taking typical students, would you like to talk a minute about "GANAS"?

Mr. Escalante: GANAS is a strong word in the language the kids use at home. It means desire. I tell the kids that once you have GANAS, the rest is easy. The only thing we need from you is just put a little time and desire to do it.

Dr. Kester: Let's proceed to the research-based statements taken from the sources mentioned earlier, and the listing of those statements that comes from your calculus students who filled out a questionnaire in May 1990.These statements are listed in rank order beginning with the statement judged to be most like you. At the top of this list is, "Mr. Escalante is often funny or humorous." My first question is, "Does this ring true to you?"

Mr. Escalante: I believe we have to have fun, we have to have jokes to capture the attention of these kids.If the teacher is dry and walks into the room and walks straight forward to say, "Open your books to page so-and-so" he's not going to get the response I'm looking for. The teacher has to havethree basic things to be able to capture the attention of these kids. Number one, he or she has to know the subject. Secondly, to motivate, I have a lot of fun, making jokes to motivate these kids. Thirdly, there must be a positive relationship between the students and the teacher. And as I've said, I like to keep them for three consecutive years.

Dr. Kester: So the students in your calculus class who filled out these questionnaires were with you for three years?

Mr. Escalante: Yes, they were. In some cases it was more than three years. I have cases in which kids from junior high come to me and say, "I want to be in your class."I say, "Okay, no problem. You can be in my class."But immediately the kid says, "I'm going to be there for only one semester." TI.at's when I have to say "No, the math you take from me is not one semester or one year. It's going to be three years.After you see whether you can learn from me, you spread theword into the other schools that doing math is fun."

32 ,:15 411

Dr. Kester: The third statement is, "Mr. Escalante believes my first priority is to learn."

Mr. Escalante: Yes, any kid will learn. Any kid can do it.I tell the students, "I think you can learn. You can prove to me that you can do it.I do not believe in 'gifted' you don't have to be gifted to be able to learn." That will always be my philosophy.

Dr. Kester: The next one is, "...(He) puts academics first."

Mr. Escalante: True.It's okay for youngsters to participate in sports, but that has to be limited. In order to have academic achievement, I say to the kids, "Look, you guys, realize that what you're learning in this class is something your going to be applying later on in your life." Mathematics is the language you have to learn. That's why academics come first. We have to live according to the new technology. You have to have chemistry, physics, biology, and so on for high tech careers, and the language is mathematics. You can play football, basketball, whatever, but the first thing you have to keep in mind is that education is the ticket to success.

Dr. Kester: Well, they have certainly gotten that message, according to how they answered the questionnaire. "Mr. Escalante expects me to work hard."

Mr. Escalante: In our classroom, we say you'll attain success only if you work hard. Nothing comes easily. You have to produce. You just set up goals and go for it. At the same time, I teach values in the class.I say, "Look, it's not just to learn math-it's also to learn respect including respect for the flag."

Dr. Kester: Now, the second highest-ranked statement that they gave us was, "Mr. Escalante expects me to achieve and do well in math."

Mr. Escalante: I always say that I build the confidence in the kids. I say to them, "Believe in yourself. If you believe in yourself, you're going to be able to do it and you're going to think positively."Believing in yourself means building confidence. If you believe in yourself, that's a giant step to success.I expect from you much more than you think you can do. Dr. Kester: The next one is, "Mr. Escalante has helped meunderstand that employers will want me to have a solid preparation in math,reading, writing, and problem solving."

is not interested in what Mr. Escalante: When you look for a job, whoever might hire you your problems are. He isinterested in what you know. I spent more than eight years working in industry. I know employerslook for productive and effective employees. Teachers need to givechildren the solid preparation they'll need to get and hold good jobs. 0 Dr. Kester: They also say that you are both "enthusiastic"and "energetic."

be with a lot of energy. A Mr. Escalante: When the teacher walks into the room, it has to teacher has to have the energy of the hottestvolcano, the precision of the best calculator, and the memory of an elephant.Every time I walk into the room I remember exactly where I left the daybefore. Besides that, I always have fun with the kids.I do say that I bring to the school and theclassroom GANAS every single day.

attend class, come to class on time, Dr. Kester: They say you expect each of them, "...to and meet the assignment deadlines."

Mr. Escalante: One of the things that's important in aclassroom is discipline. They can come to my early-morningclass 10-20 minutes or one hour beforeit starts, because they always know the teacheris always there one hour early. I'm in the classroom at 7 o'clock and theyknow I'm the last one leaving the school. School ends at 3 o'clock and I'mstill in school until 4 or 5 o'clock in order to help these kids toachieve what they have in mind. I know athome they don't have the help they need, so I have toprovide that help after and before school.I ask the kids to be always ontime.If I do not control the classroom this way, later on thepicture will change. The kids willgive up or drop out. WhenI have this control, the students aregoing to produce and they're going to be able to continue.

Dr. Kester: This you alluded to earlier, "Mr.Escalante is an excellent mathematician."

34 Mr. Escalante: Well, it's no trick doing math. The first teacherwe have is the experience. I learned math by doing it. Andmy grasp of my subject has deepened with more than 20 years of teaching experience.

Dr. Kester: Before the first bell even rings for thenew year, you have everything already planned. You have prepared all ofyour worksheets and all of your presentations before your first classeven meets.

Mr. Escalante: I have my lesson plans madeup 20 weeks in advance.I have the file cabinets ready to use for the 20 weeksat the same time, making corrections and changing problems to really go according withthe new technology. That helps to improve my teaching in first place andin second place prepare these kids for life. I do have myown handouts and my own problems. That doesn't mean I don't use the booksI douse the books, because I feel that the textbooks are a good reference for the students, butI feel confident when I use my own papers.

Dr. Kester: For the next one, your calculus students said, "Mr. Escalanteis cheerful."

Mr. Escalante: Well, if the kids said that, it's because I'm really proudof my students.

Dr. Kester: This you touched on earlier when you mentioned values; ".. .expects me to be honest, courteous and show respect for others."

Mr. Escalante: We have to teach our kids values, the great thingswe have in this country. It's not unusual for me to start talking about the patrioticsymbols and the great things this country did and the great men we had.I teach responsibility.

Dr. Kester: You mentioned this earlier also, "...has helped me see that education is important."

35 Mr. Escalante: Education is the ticket to success. It's the only way we are going to be able to keep with the other countries. I feel that 10-15 years old is the critical age. That's when we have to motivate these kids, to show that through education you can achieve, or get a job easily, or preparefor a profession, going to a four year college or three year college.I don't require all my kids to be majors in chemistry, physics, mathematicians, or pre-med. No. But Itell them, 'you could be a good technician, but you need education.'

Dr. Kester: They say you call "...attention to diagrams, graphs, photos, or illustrations that not only relate to the lesson but also help me learn and remember."

Mr. Escalante: It's important to visualize mathematics to make it come alive.In my teaching, I do use drawings and some practical examples and so the student can picture it. Also, every time we gothrough word problems I ask them to tell me what kind of picture or graph could be made of it. 'Can youvisualize what the problem is?' I ask. Doing this every day, the kids getfamiliar with that approach; they know a diagram or a picture helps yousolve the problem.

Dr. Kester: When I was in your Algebra II class, I saw you grab your chalkand draw a diagram on the floor instead of putting it on the blackboard. Thekids got up out of their seats to gather around you.Judging by their faces, they were asking themselves, "Now, what's he doing this time?"

Mr. Escalante: I try to capture the attention of the kids, it's true.The other day, for instance, I walked into the classroom with my hands in mypockets. The whole class was looking at me because I was walking with my twohands inside my pockets. Immediately some of the kids said,"What do you have in there?" My answer was "Nothing." "You gotsomething in there!" "No, nothing:" "He is going to show ussomething." That's what I expect from the kids: "He is going to teach us something new,that's why he is hiding something."It's just to bring mathematics alive and capturethe kids' attention.

Dr. Kester: "...'encourages me to try harder by reminding me thatpeople beyond our school are paying attention to how well we do."

36 Mr. Escalante: One of things that's important in the classroom is to tell the kids, "Look- - people are always watching you, looking at you, learning from you. You're an inspiration, did you know that?" And the kids ask "Do youthink so?" "Yeah, yeah." I tell them and I know you're going to make it. Also, I use examples.I say you know the famous baseball pitchers have to pace themselves. "Don't look back, maybe something is gaining on you." If you really put little GANAS, your mom, your teacher, everybody will be proud of you. You really made it.

Dr. Kester: The next one is,...has taught me rules and principles and the conditions under which they apply so I can solve math problems."

Mr. Escalante: Absolutely.That's building up their skills so they can get the answers easily. I'm really pleased with that kind of remark from the students.

Dr. Kester: One of the things that was brought out in the movie, "Stand andDeliver" relates to the next one. "Mr. Escalante has helped me understandthat I learn more in rigorous, tough courses thanin courses that are easier."

Mr. Escalante: When you have an easy class, the students like to take it easy,kicking back. But if you make it a little difficult gradually, the kids aregoing to respond. What I'm doing is challenging them. That's why I say to them,"Algebra I is a piece of cake. What we aregoing to do is calculus, the next one.'" So really what they are doing is Algebra II, but towardcalculus.It's challenging them. I have good feedback from doing that.

Dr. Kester: The next one is, "...Mr. Escalante is friendly towardme."

Mr. Escalante: One of the things that's important in teaching isthat you have to show love, unlimited love but with the one kind of compensationfor me: they have to do their assignment, their homework. When I showthat kind of appreciation or love, the kids give you the feedback. But I have tocultivate that for the three years and so I say to them,you're my friend. I'm just the coach. Since you're my friend, you can do any mathematicalassignment that I ask you to do.

37 Dr. Kester: .gives me a lot of math problems to do." You work them prettyhard, don't you?

Mr. Escalante: Yes sir, we have a minimum of 20 problems a day in theclassroom, so the kids understand what's going on. Once taey get the picture,they're going to be able to do their homework I give more than normallythey have to do, because practice comes first. Gradually, year by year, I increasethe number of problems the Kids have to be doing in the classroom.

Dr. Kester: You're accelerating these students too. In your journalarticle, you mentioned that you're getting these students through six yearsworth of math in three years.

Mr. Escalante: Yes, I do, actually; I put them on the spot. Ten to fifteen yearsold is the initial period of puberty. They develop mom rapidly than in anyother phase of life. I take advantage of that. I say, these kids havethe chance to be able to produce, because the 10-15 yearsold, they think in a complex way. I take advantage of that doing math.

Dr. Kester: You alluded to this before, "...helps me enjoy math."

Mr. Escalante: Oh, it's fun. You have to have some jokes inthe class, and do some shortcuts. I make them believe I'm a magic manand they're going to be magic men too if they do these shortcuts. Math has so manybeautiful things to be able to do to capture the attentionof the kids. I do these things and they enjoy it. They like to do math.

Dr. Kester. "...has encouraged public recognition forstudents who succeed and promoted a sense of school pride." You weresetting up competitions even in La Paz, Bolivia. Now it's "Beat EducationalTesting Service (ETS)!" But you've always used competition and publicrecognition, haven't you? Mr. Escalante: Yes. This way it's much, much better, because everytime we have a competition in mathematics, we are the first to sendanybody to be in the competition from that school. But we do concentrate more onthe Advanced Placement Exam because I feel that's a good gate, a way toanalyze what we are doing wrong in the schools,also one way to find out the corrective actioa to be able to work towardimprovement in academics.I feel that the Advanced Placement Test is a first-class test. I say tothe kids that when you go to take that test you'regoing to "Beat ETS, Beat ETS, Beat ETS!" AlsoI make them believe that Garfield HighSchool is the only school that could compete with the Japanese. Thekids build that idea starting at the 10th grade. So when they're in the last year, theirsenior year, always they say, "Do you think we can beat them?" "I think so,I think so." You have to push a little bit more and you will see themachieve.

Dr. Kester: In talking with your program staff, GeorgeMadrid, Paul Powers, and Kevin Galvin, they said that the numbers look evenbetter this year. They always look good, but both the number of studentstaking the Advanced Placement Exam in calculus, and the number passingcontinues to look just great.

Mr. Escalante: We have to improvethat's one way to look atit.This year we have lots of calculus students ready to take the test, and eventhough I haye so many things to do besides my teaching assignments.We have so many visitors from different parts of the country, differentschools, teachers, even people from Japan are coming to see the techniques we useto motivate these kids. That takes away. my teaching time.Besides that, I get invitations from different states to share this kind of program wehave. I feel obligated to do that. Even though I'm really proud of thestudents, the test results would be much, much better if I just concentrated on mystudents as I used to do.

Dr. Kester. "...has helped me set higher goals formyself in life."

39 r)I Mr. Escalante: You know in East Los Angeles, kids don't have too many expectations of themselves. I say to them, "You could become a teacher, you could become an engineer, a doctor or anything you want, becausethrough the program I have and through education you're going to see tomorrow is a better day, you're going to be much, much better than me." The kid keeps that kind of picture in mind, and it pays off. I'm proud to say that at this stage I have engineers and doctors who are former students.In fact, the Advanced Placement computer teacher, Roy Marcus, here at Garfield, is a former student of mine from 1982. He's well known as one of the top teachers in California in computers. Roy says "we have too much competitiongoing with you."

Dr. Kester: The next statement they say is like you is, "...has helped me see myself as a winner."

Mr. Escalante: Always, always. I expect my kids to be winners. You expectkids to be losers, they will be losers. If you hold them accountable for whatthey do, they will amaze you. I have seen it happen at Garfield High Schoolduring the last 18 years.

Dr. Kester: "Mr. Escalante believes in me."

Mr. Escalante: That's right, I do 100 percent trust in the kids. I do say thisin the clas.s,--"I believe in your success, I believe you're going to do it, I believein you on a one-to-one basis." Eventually the kid starts believingthat.

Dr. Kester: "...(He) captures and holds my attention." This was somethingI noticed right away when I was an observer in your classes. It seemed to methat you didn't just ask for my attention, you took it.It was next to impossible for me not to attend to you and what you weretalking about.

Mr. Escalante: Yes, a teacher has to have that. I know what the kids aredoing even though I'm not looking at them.When I'm in front of the students at the chalkboard, the first thing I have to do is to have to get theattention of each of my students.In the beginning it looked difficult. Nowit comes naturally. I do have, I should say, that quality.

40 Dr. Kester. Yes, you do, you certainly do. The next one is, "...requires thatfaster learners put forth effort too; he won't let them just coast."

Mr. Escalante; Yes, you don't need to be a smart teacher to know which ones arecatching the whole image at one shot. So, I have to takeadvantage of those and give them a little bit more to keep them producing,because if I ignore them I . might ' have to keep motivating them and give them a little more. But it's v ua,ng wiiat they learn. In the end I'mreally proud of these kids doing these wonderful things.

Dr. Kester: You let them work as teams, too, don't you?

Mr. Escalante: It's really important to work in teams. That comesfrom my experience in industry. I found that cooperation and communication are necessaryto the smooth running of a business. It's cooperativelearning and so we have to teach that kind of environment in the school.What I do is group four or.five kids. The weak kid is the leader. I say, you'regoing to be the lead man or lead lady, so you'll answer any questions. Sometimes the weak kids says, "I don't understand too much." I reply, that's nobig deal, you come in the morning or in the afternoon and I will teach youwhat we're going to be doing. Working in groups is productive; theylearn more than on a one-to- one basis.

Dr. Kester: "...gives me the help I need when I get stuck."But how do you knoW when they get stuck?

Mr. Escalante: From the face of the kid, immediately.

Dr. Kester: But you have large classes. Last summerI saw sixty or more students in your Trig/Math Analysisclass.

Mr. Escalante: Yes, I had about seventy-three students.

Dr. Kester: Seventy-three students! Mr. Escalante: What I do is simple. When the class is working and the kid starts tapping his pencil on the paper and looking to the sides, I know the kid is a little frustrated.In order to avoid that kind of negative response,I initiate a conversation with him, with a joke. The kid starts building confidence, and I go step-by-step, the kid sees what the problem is. Then I give him another one similar to that, and build up his confidence.

Dr. Kester: "...has helped me understand that I can become qualified for any job I want."

Mr. Escalante: Anybody could be qualified for a job they want if they put just the GANAS into it. When they work in the classroom, they build that. In order to help students build strong belief in themselves, I use posters of famous players and examples of great people. I always say that you guys have math in your blood. You know the Mayas were the big mathematicians. So, all you have to do is use your logic, and you're going to be able to succeed.

Dr. Kester: A lot of the statements that we are getting to now sound similar to ones we've talked about before. This is because statements were taken from different sources. One review of research concerned motivation, while another one focused on teaching and learning.So, some statements are similar but not exactly the same. This next one is similar to earlier ones, too. "...(He) expects me to spend a lot of time on math."

Mr. Escalante: Yes, it's true. Math is just practice.

Dr. Kester: "...has helped me learn how to think through a word problem before I begin working on it; to analyze the challenges I face and explorealternative strategies before I start to work."

42 Mr. Escalante: That's one of the things that's important. If I'm the quarterback, I'm not going to throw the ball to just anybody. I have to lookfor an open receiver. That's exactly how to solve a problem. You look at theproblem and know what kind of tool you need. Use it to solve the problem. You don't have to memorize formulas. The formulas are tools, and the tools becomefamiliar to you using them every day.Each student does not have to be a great mathematician. Mathematics is just using tools correctly.

Dr. Kester: Now, earlier we had an item that was higher in this list that said,"...has helped me set higher goals for myself in life", and this one is similarto it. But it's interesting to notice that this one is further down thelist;"...has helped me set higher goals for myself in math."

Mr. Escalante: I ask myself what is the future for my students? The future isin chemistry, physics, biology, computers, electronics, and other high techfields, but the language is mathematics. Math will open the doors for you.

Dr. Kester: "...has taught me to estimate answers to math problems so thatI can reject unreasonable answers and know when an answer is 'in the ball park'."

Mr. Escalante: That's correct--math is just estimation. Mathematics is just toapproximate. So I look at the kid and I say I think you are 14 or 15 yearsold. And the kid says "No, I'm 14.""I'm just estimating, you know?" I say, look I have $20. I could spend only $2. I'm hungry, I have to eat so Ihave no choice- - I have to go to McDonald's if I want to spend only$2. I'll spend only $2 so I can save $18. This is what math is. That's what youdo if I ask you what time it is. You might say you think it's 12 o'clockwithout looking at the clock. That's math estimation.

Dr. Kester: "...takes us through the steps needed to solve aproblem and explains the purpose of each step."

43 Mr. Escalante: This is the nice thing in math. Step-by-step and you come out with the right solution. You really feel satisfaction. I don't want the kids to be sloppy. I want them to follow the steps they have to know. If you getstuck, go to the picture, go to the graphic. If the graphic does not help, you try to find some other appropriate tool. It's going to be a formula or an equation. You have to be practical. This is the only way to mastermathematics.

Dr. Kester: "...has helped me become more interested in math."

Mr. Escalante: Kids enjoy listening to me talk about the history of math. In thebeginning, for instance, who invented the number one, number two, and soon? Who started with the numbers? I draw a picture with a square and I say,"The one came from here, from the square andthe two came from here" and so on. That's fascinating and the kids say, "I like to do math, I like math."

Dr. Kester: "Mr. Escalante understands the world I will face after high school."

Mr. Escalante: Naturally. Nothing comes easily. You have to be prepared forlife and work. Your mom and dad will not always be helping you.You have to know how to fill out a job application neatly, because if the employer cannot read the name of the applicant, they won't even call for aninterview. So, you have to be neat, you have to beable to answer the questions. For instance, if you're applying for a job in electronics and theyask you what's your hobby, you shouldn't sayfishing.No, you have to say I like electronics, I like to build this and that.If you say I like fishing you're probably not going to get the job. These things you have toknow. That's one of the things I was sayingin the beginning. That's why we have to teach values, we have to teach them something elsebesides the subject we are teaching.

Dr. Kester: "...helps me plan and strive for excellence."

Mr. Escalante: Absolutely. That's exactly what I was going to say, I wasahead of you.

Dr. Kester: Yes, you were ahead of me, that's right."...expects and rewards my academic success."

44 Mr. Escalante: I have good connections with McDonald's. They provide coupons. For instance, today two kids were waiting for recognition, and they told me, "Today is my birthday" they know I'll present the coupon for their birthday. But if they do well in a test, or if I see improvement, they know they'll get a jacket with a bulldog (for the advanced placement calculus students) or a t- shirt for the summer, or a hat printed with GANAS. They are little minor things which really motivate the kids to keep on going.

Dr. Kester: Now, what does the term "Stand and Deliver" mean? You use that phrase frequently; it was even chosen as the title of the movie. But, what does it mean to you, Mr. Escalante?

Mr. Escalante: That phrase means you play defense on the test. You use all the intelligence and all the information you have stored in your brain. You prove you know math. You stand and take the test and you present it to the teacher. You deliver what you've learned. That's the meaning for me. When the kids "Stand and Deliver," they have the background, the knowledge to be able to answer any questions related to this subject.

Dr. Kester: I noticed in observing your class and in talking to you and others in the project that you do a number of unusual things. For example, you get students up to the front of the classroom, then when they are the center of attention for the whole class, you fire math questions at them. Do you have a name for that particular teaching technique? Mr. Escalante: That's another way of showing whether you can Stand and Deliver. Now also it's to prove you're not afraid. Every time I talk to you, you have to look at me the way I look at you and answer the questions. The fans used to call Jerry West, the famous basketball player, Mr. Clutch. Why? Because when the team needed the extra point during the last seconds of the game, they'd throw the ball to him, he'd shoot and make the point. I spoke with him and he said even when he didn't have a game scheduled, he took the basketball and shot it at least 500 times. I said to the kids, I expect from you the mile reflexes. If I ask a question. I expect from you the correct answer, and right away. That creates a really kind of combination in their brain. The kids expect the question, and they know they have to answer immediately. They cannot reject the ball. That builds a good framework for mathematics and thinking.

Dr. Kester: There is no place for a student to hide either, is there?If they don't do the work and learn what you expect them to learn, they risk being embarrassed in front of the whole class.

Mr. Escalante: No, they cannot, because if they don't answer the question I have to give them a second chance. That'll be a one-to-one basis after school, but with the condition that tomorrow I'll put you on the spot again. The kid says, 'go for it!' At the beginning they're afraid; at the end they like to be in front of the class and answer questions. Another thing that we do is we give values to seats. For instance, whoever reaches this chair is an A, that oneis a B, the other is a C. I ask questions and whoever is seating in the first chair should know all the answers, otherwise they'll gradually go back.

Mr. Escalante: There is a challenge to be able to stay up front. One of the students asked me, Why don't you put two As and two Bs, whyonly one A?' It's just to stimulate them, to motivate them to study.

46 rid Dr. Kester: Well, it has been very enjoyable for me to work with youagain, Mr. Escalante. Our assignment here was to focus on thedevelopment of the "instructional manual" that, according to the grantapplication, was to describe your teaching and motivating methods. To save youtime, my approach was first, to ask your students to identify someresearch-based statements that they judged to be like you,and then to use those as a prompt to you, to get you to discuss yourteaching and motivating methods. This approach has provided us with information not onlyfrom you but also from your students. You have responded tothe first thirty-eight items that your students say are most like you. Are there other things thathave not yet been mentioned that need to be mentioned?

Mr. Escalante: One of the things I have to mention is that to have successin teaching, you have to have the administrators on your side. Besidesthat, you have to have commitment from the parents, because school alone cannoteducate. I didn't want you to come to a conference I had with parents,because that changes the picture. The parents don't feel confident whensomebody else comes to the room. The first conference we have with the parentsis two weeks before the start of the new school year. These are the newunmotivated kids, so I call on the parents to get their participation, their comment tohelp me out. Tney have to sign a contract with me in order to helpthe students to attain success. The first day, wepotluck, we only socialize: students, parents, and teachers. The second meeting is between the parentsand the teacher only, no students involved.That's when I ask the parents to help me out,and I usually say I need for you to follow three steps. NumberOne is every time you talk to your kid, talkwith love, without any limits. Number two, when you talk to your kids I want you toput in one hand discipline, andin the other one love. If you maintain the balanceyou'll promote responsibility.

47 6 ,*1 Mr. Escalante: The last thing is more difficult for you. You must understand your teenager. If you cannot understand your teenager, you have to call me, because you and I together will help this kid to be educated, and tomorrow he is going to college. Another thing I say is, as soon as your son or daughter gets home after school, don't be dry. Ask him or her with love, "What did you do in school? How was your class, did you play games?" Try to start a conversation and build that kind of relationship with your kid, because I don't want a breakdown between the parents and the child. And another thing I ask is when your kids approach to talk to you, listen. Wake up. It's an opportunity knocking at your door to helpthem to be educated. The other thing is, when the kid talks to you, don't give quick answers. Don't talk about your concerns, help him/her out to be able to find their own answers and don't lie, don't ridicule.That way, you'll build an environment of happiness, love, understanding, and this way you are not just showing love for your students, you're showing what I call sensitivity toward something which belongs to you--your child. That day, the parents understand. Igive one more potluck the following week and we go overagain the three points and this time, a little bit more precise. With that we start buildingmutual support, and the kids start giving me the feedback.

Dr. Kester: Can you think of anything else that you might mention?

Mr. Escalante: I have been teaching 15 years in East Los Angeles. I find that itis good to associate with the people whose children are going to be in my classroom. There's a positive response. I also enjoy having the kids come to myhouse.

Dr. Kester: Yes sir. Well Mr. Escalante, I want to thank you again, it'sbeen a real pleasure working with you over the last couple of years.

Mr. Escalante: For me it's been a great honor and so we are going to have tokeep working and give a big plus for education.

Dr. Kester. Yes sir. This has been an interview with Mr. JaimeEscalante. Thank you very much for joining us. DiEtussion

One ancient school of thought emphasizes a person'ssubjective experience. For example, John Locke (1632-1704) wrote that people can directlyexperience only "secondary qualities" of physical objects in the external word such as colors, sounds, tastes,odors, weights, and warmth. All we know is what our senses receive and process.Locke's position was that we cannot directly experience the "primary qualities" that are inherentin physical objects such as solidity, volume, shape, and number. Later, Bishop GeorgeBerkeley (1685-1753) agreed that the only things we, as people, can directly experience are the secondaryqualities. The point is, that all we can ever "know" comes to us through ot: senses. What we"see," for example, is the result of light waves bouncing off an object, entering our eyes and beingtransformed into bioelectrical stimulation in our brain. This led Berkeley to contend--esse estpercipi "To be is to be perceived" (Christian, 1973, pp. 139-148). In other words, objective realityis not directly knowable.

Along the same line, it has been said that when a manand woman get married, the result is not one but at least three marriages. First, there is thesingle marriage recognized by the legal system. Second, there is "her marriage"the marriage asshe experiences it. And third, there is"his marriage"the marriage as he experiences it. And, as anydivorce lawyer knows, there can be enormous differences betweenwhat each spouse experiences.

In a similar way, one could say that there areseveral general Jaime Escalantq classroom experiences.First, there is Jaime's classroom experience as onecould capture on videotape. Second, there is Jaime's classroom as he experiencesit. And third, there is Jaime's classroom as his students experience it. In addition, thereis Jaime's classroom as experienced byobservers; in this case, Angelo Villavicencio, Cathy Lum,and others, including the current writer.

Creating an Overall Conceptual Frame of Reference

Escalante's calculus students have identifiedthirty-eight statements as more like him (seeTable 5), discover or but this is hardly parsimonious. According to"Occam's Razor," care must be taken to invent the simplest explanation. The followingdefinition may be helpful: Occam's Razor (Also called the Principle ofParsimony). One of the fundamental principles of (the) scientific method. It states that,all else being equal, the simplest explanation is the best. That is, in developinginductive hypotheses, the simplest hypothesis which accounts for all relevant datais more likely to be true. Named number of after the scholastic philosopher Williamof Occam, who phrased it: "The entities should not be needlessly increased."(Christian, 1973, pp. 381, 502).

49 Fi , *

Inventing iconceptual frame of reference is riskybusiness. There is always the possibility that it will saylas tputh or more about.the inventor than thephenomeCia being studied. Still, in this case, to leave ;theear der withEscalante. 's calitius stu Tents' top thirty -eight statements, even though they .$ c have pasectttister by a revieyibyBeate,is to leave the investigation, to an important degree, unfinishlt. )311 the tand, the fdplAitking conceptual taxonomy should be considered asonly 4 otierj.4 tzttie wosioing.hypothesis; Only one sugksted taxonomy amongseveral that might be offered. In thislaxonomy it at first appears that there are four categories into which thethirty-eight statement can be placed. These categories are: Personal Characteristics; Cognitive Restructuring; Teacher Expectations; and Mathematical Skill Development

But, on further consideration, it will be seen that the category,"teacher expectations" may be considered to be a special case within the ibrger category of"cognitive restructuring." This further simplifitalion 4 vides us with only the following three major and one minOr category.(See Table

7.) After gimp g, those categories are: A

: 1. Pei sonal Characteristics; 2. Cognitiy kites taring,. including Teacher Expectations; and 3. Matiternattal S Development,i.

, oe; An advantfge of this taxonomy Is that three of the fourcategories"Personal Characteristics," "TeacherExpectalions&"..tand "Mathematicalkill Development"are immediately clear and understandable.drily "Orte--"Coknitive Restructuring "may need to be defined and discussed at any length. In any case, threet4ajor categories, are considerably more parsimonious than thirty- eight unrelated statements. , The first major category :Personal CharacteristicS"is self explanatory. One teacher can be more or less "funn41," "enthotutic," "energetic,""cheerfUl," or "friendly" than another. One may appear to be a better inathen4tician:than another. One mo"capture and hold a student's attention" better. And one mai to"believe in his students" More.

50 tl Descriptive Statements TABLE 7 Identified as More Like Jaime Escalante and His Teaching ProposedPersonal Taxonomy Characteristks of Thirty-Eight Cognitive Restructuring Mathematical Skill Development is isenthusiastic3often energetic4 funny or humorous2 putsbelieveshas helped my firstme understandprioritywill iswant to that learn'0 me employers to have a solidacadeMics preparation first" in callshas attention taught me to rulesdiagrams,relatephotos,learn and to principlesandor graphs,the illustrations remember32 lesson but thatalso nothelp only me ismathematicians ischeerful6an friendly excellent toward me7 has helped me seemath, thatimportant13solving12 reading,education writing, is and problem gives me a lot oftheyand dos'problems33math the apply conditionsproblems so I can to undersolve mashwhich attentionscapturesbelieves and in me9 holds my encourageshas helped me meto try understandpayingmein that rigorous, attention people that Itough beyondlearn to how coursesmore our than in courses harder by reminding well we do14 sc!tool are requiresgives me that the faster helpeffort "coast"35learners I need too; heput won't let them just when I get forth has encouraged publicstudentsthatsense are recognition easier15of who school succeed pride16 for and promoted a takes is through thepurposesolve"stuck"36 steps a needed pre'of each lem to step37and explains the Proposed Taxonomy of Thirty-Eight Descriptive Statements Identified as More Like TABLE(Continued) 7 Jaime Escalante and His Teaching Personal Characteristics Cognitive Restructuringhashelps helped me enjoy me set math" higher goals for myself in Mathematical Skillhas Development helped me learn beginthroughhow o working think a word on problem it; to analyze before theI hashelps helped me see me myself understandlifel8qualified as a "winner" that for I anycan jobbecome I want20 19 has taught. me iotoalternativechallenges estimate mathwork38 problems answers strategiesI face and soto that beforeexplore I can I start reject U, hashas helped helped me me set become highermath21 moregoals interestedfor myself in in whenunreasonableballpark"39 an answer answers is "in andthe know helpsunderstands me plan the and worldmath22 striveschoo123 I willfor excellence24 face after high Teacher Expectationsexpects me to achievework hard and do wall in math26 expects thatme to I canattend andtime, math28class, will and learncome meet a to thelot assignment deadlines27 class on of S S Proposed Taxonomy of Thirty-Eight Descriptive Statements Identified as TABLE(Continued) 7 More Like Jaime Escalante and His Teaching Personal Characteristics I Cognitive Restructuringexpects me to be honest, courteous, and to Mathematical Skill Development expects me to spendexpectsshow asuccess3I respect and rewards for others29 my lot of time on math39 academic 2 Evaluator's classroom observations1990, p. notes; 7 NEA, 11USDOE,I2USDOE, 1987, 1987, p. p.58; 81 NEA, 1990, P. 8 22NEA,2IUSDOE, 1990, 1987, p. 7 p. 35; NEA, 1990, p. 9 33USDOE,32USDOE,3IUSDOE, 1987,1987, p.pp.p. 3834; 35, NEA, 58; NEA, 1990, 1986, p. 4 p. 22 6NHA,4NEA,3NEA,5NEA, 1990,1986, 1990, p. 820pp. 7, 8, 10 I5USDOE,I4USDOE,13UISDOE, 1987,1987, 1987, pp. p.p. 75; 15;43, NEA, NEA,57 1990, 1990,p. 9 "NBA,26USDOE,25USDOE,24NEA, 1990, 1986, p. 1987, 9 p. 18; pp. NEA, 35,14, 58;15; 1990, NEA, p. 6 1990, p. 8 37USDOE,36USDOE,3511SDOE,34USDOE, 1987, 1987,1987, p. pp.p. 41 45;14; 14, NEA, 37, 78 1990, pp.p. 7 8, 9 lUSDOE,7NEA, 1986, 1987, p. 20;p. 39; NBA, NEA, 1990, 1990,pp.p. 9,10 8 IINEA,I7NEA,16US1DOE, 1990,1990, 1987, p.p. 97 p. 57 pp. 3, 4 281.1SDOE,nUSDOE, 1987, 1987, pp. p. 35;35, NEA,59; NEA, 1986, 1986, p. 22; NEA,NBA, 1990, p. 89 39USDOE,3211SDOE, 1987,1987, P.p. 2529 9USDOE,I°USDOE, 1987, 1987, p. 35; p. 58;NEA, NEA, 1986,p. 22;1990, NEA, p.8 1990, p. 9 "USDOE,I9USDOE, 1987, 1987, p.p. 35;35; NEA,NEA, 1990,1986, pp.p. 15; 5, 9NBA, 1990, p. 9 "USDOE,30USDOE, 1987, 1987, p. 59;pp. NEA,15, 75 1990, p. 20;pp. 7,NEA, 11 1990, pp. 4, 9 However, the boundaries around the categoriesshould not beseen as solid."Is an excellent mathematician" might better fit within"Mathematical Skill Development." Or perhapsthis statement belongs under both categories, "Personal Characteristics.' and "Mathematical SkillDevelopment." The same could be said of the phrase,"captures and holds my attention." Similarly,"believes in me" could possibly be listed undernot only "Personal Characteristics" but also"Cognitive Restructuring."

Whereas "Personal Characteristics" willvary greatly from teacher to teacher, probably nearly all teachers of high school calculus think theyuse most, if not all of the teaching methods listed under the third major category, "Mathematical SkillDevelopment." Wouldn't every math teacherreport that he "takes his students through thesteps needed to solve a problem and explains thepurpose of each step?" Wouldn'tevery teacher say she "helps her students learn howto think through a word problem before they start to workon it?" Wouldn't every teacher say he "gives his studentsthe help they need when they get 'stuck'."Wouldn't every teacher say she teaches herstudents "rules and principles and the conditions under whichthey apply?"

While it may be unfamiliar to many educators, the term "Cognitive Restructuring" iscurrently in use by psychologists and counselors.Cognitive theories have a long history; cognitionhas been and still is recognized as related to humanemotion.

" ..Aristotle... suggested that human beings . .. can make sensory judgments . ..of things as being good or bad for them; thisestimate arouses an emotion, liking, or dislike. Thomas Aguinas...followed Aristotle in this explanation of emotional arousal...

Theorists of all persuasions usuallyagree that anger or fear are aroused when a situation is interpreted as annoyingor dangerous. Many insist that such arousal is programmed into the nervous system during evolutionary prehistory and serves. biological survival. For cognitive psychologists,every emotion is aroused by knowing something and appraising it.No doubt, some appraisalsare preprogrammed: i n f a n t s like anything sweet the fir s t t i m e they taste it...

But older children and adults appraise what theyencounter not only as it affects their bodily well-being but as it affects themas persons. The child is angry when teased by buddies; the young man, when his pals showhim up before his girl... (Corsini, 1984, pp. 242-243).

54 Further, Cognition is recognized as being essentialin the counseling process. Cognitive therapies are a loosely associated groupof approaches that stress the importance of cognitive processes asdeterminants of behavior. They maintain that behavior and emotions result largely fromone's appraisal of the situation, and that, since appraisal is influenced bybeliefs, assumptions, images, and self-talk,these cognitions become the targets of therapy ...cognitive therapies differ from ... (traditional psychotherapies) in severalimportant respects ...First, they stress the primacy of cognitions overemotions and behaviors. Since they believecognitions instigate behaviors and triggeremotions, they maintain that the alterationof dysfunctional thoughts, assumptions,and beliefs should be the principle concernof cognitive therapies, inasmuch therapy..In the broadest sense, most therapies are as they seek to bringabout changes in the client's privateviews...cognitive therapy differs from ...(other) therapies in more directlyattacking faulty assumptions, beliefs, and thoughts, andin specifically teaching coping skills believed to be missing from the client'srepertoire (Corsini, 1984, pp. 245).

Different writers have used slightly differentwords to describe their approach. For example:

Alfred Alder expressed his convictionthat neurotics base their self-defeating behavior on fictional beliefs ...therapy...consisted (in) ...changing such self-programming ...Norman beliefs...Maxwell Maltz stressed ... proper Vincent Peal stressed the importanceof thought control ...Jean Piaget ... observed that all adaptation occurred through twoinvariant processes: assimilation and accommodation. Accommodationis the process by which personsform concepts, called schemes,which guide behavior. Assimilation isthe process of recognizing and applying existing schemasin coping with environmental demands. Not all schemas are correct guides tobehavior: inadequate or erroneousschemas contribute to maladaptive behavior.Piaget's cogent writings were influentialin causing. ..(many) to recognize the importance ofcognitive factors. (and) stressed the Albert Bandura .(helped) establish social learning theory ... importance of learning from others throughimitation, and recognized the key role of such cognitions as attention, symbolization,expectancy, internality, andself- efficacy.Bandura's powerful research base ...(helped to establish) the relationship between cognition andbehavior...Michael Mahoney and Diane Arnkoff list Albert Fills' rational-emotivetherapy (RET), Aaron Beck's cognitive therapy, and Donald Meichenbaum'sself-instructional therapy (1975) as examples of cognitive restructuring. The first twotherapies attempt to restructure beliefsand assumptions, while Meichenbaum'sapproach attempts to change self-verbalizations (Corsini, 1984, pp. 245-246).

couple of examples of case With this brief introduction to thetheory, it may be helpful to present a practice. Psychologists studies that illustrate how cognitivecounseling approaches work in actual psychotics "live are fond of saying thatthat clients who are neurotic"build castles in the sky" while in them," meaning, of course, thatpsychotics are more maladjusted than areneurotics.

55 This first example deals with the more extremely irrational beliefs of a psychotic 14 year old boy and the cognitive intervention technologies designed to dispute and overcome those irrational beliefs.

The subject was an adolescent boy previously diagnosed as a "chronic schizophrenic" who attended a self-contained special education classroom at aregular school. Cognitive intervention included problem solving and self-instructional of erroneous client perceptions, beliefs, and self-signals. One of the boy's problems was that the other students complained that he "smelled bad." After talking with the counseling team, this area needing work was identified as his "personal hygiene and appearance."

Step one in this cognitive restructuring approach was to "identify the problem." The boy called it "teasing" and denied any awareness of body odor. In short, the boy thought he bathed as often, was as clean as other people and did not "smell bad." To dispute this,the counseling team persuaded him to make a survey of 50 people to see how frequently they bathed, washed their hair and used deodorant. The boy was surprised to learn that 47 of the 50 reported a frequency of 3.8 time per week. Having proved the boy's beliefs about his own hygiene to be incorrect, the counseling team was then able to help the boy redefine his problem as "I do not keep my body as clean as other people."

When a plan to shower frequently had been accepted but was not being followed, the team investigated.In doing so, they found an other erroneous belief. Remember the subject is psychotic; that is, schizophrenic. This time the boy confessed that he was afraid he would dieif he got water on his face. Because of his extremely irrational fear, theproblem was redefined with the problem-solving sequence and self-instructions shown in Table 8 (Gumaer and Headspeth,1985, p. 378). TABLE 8 Problem-Solving Sequence and Self-Instructionsfor the Fear of Washing

Problem-solving sequence Self-instructions ...

Step I: I need to bathe and wash my hair, but I 1. Rarely does anyone die in the shower. am afraid to get my body wet. 2. Forty-seven people bathed every day and they are still alive.

Step II:I can shower if there is somebody nearby 1. Mr. is just outside. who can save me. I will ask Mr. to stay by the door of the shower. 2. Mr. can give me "mouth to mouth" resuscitation.

Step III:I can shower at school with a teacher 1. I can handle this. nearby until I feel more comfortable. 2. I got my face wet and I am still alive.

Step IV: I will keep track of the compliments I get1. I look great. about being clean. 2. I am a handsome boy.

The boy had agreed to report to his classroom30 minutes before the first class began.While working on his fear which resulted from anirrational belief, he imagined showering whilein the empty classroom. The authorsreported:

He imagined that water was hittinghim in the face, and practiced the self- instructions associated with this step. Thisrole play caused him great anxiety, but he gradually desensitized his fear asthe week progressed. Mr. X, who supervised his showering (at school), reported thathe talked frequently to himself, saying such key phrases as "Rarely does anyone diein the shower" and "I can handle this." After two weeks of showering at school,the boy began spontaneously showering at home. At this time, he also reportedasking his father to buy deodorant and shampoo and using his brother's hairdryer. Several faculty members commented on his improved hygiene.He also began to come to schoolwearing more attractive and "faddish" adolescent clothing(Gumaer and Headspeth, 1985, p. 377).

behavior, lets turn to From this rather extreme example ofincorrect beliefs and their influence over inappropriate aggression of a the next case study. This one dealswith the more typical problem of teenage boy.Frequently, aggression toward peersin school is combined with defiant or focus will concern oppositional attitudes and behaviors towardadults, but for our purposes here the only aggression toward peers.

57 7E The student was a 15-yearold, ninth-grade male studentof average intelligence ... home for boys, having been removedfrom The student lived in a community group and oppositional his mother's residence becauseof his long history of aggressive behavior. He attended mainstreamhigh school classes and had aC to D average in his courses at the time of referral... . The student's behavior at the grouphome has posed so serious amanagement problem that the directorviewed the counseling referral asthe last attempt at behavior before it became necessary totransfer remediating the student's aggressive (Kiselica, 1988, p. him to a residential treatmentfacility for juvenile delinquents. 306.) helping me boy develop his Again, the cognitive counselingapproach included metacognition, intervention used the ability to think about his thoughts - -aswell as his actions. The counseling instead of the cognitive more easilyunderstood terms of "before","during", and "after" (BDA) The author wrote: behavioral terms of "antecedents","behaviors", and "consequences." with the student on his BDAcards was observing One fulfilling result of working interpretations of events him as he discovered, for perhapsthe first time, how his behaviors, how consequencescould serve to strengthen could elicit self-defeating BDAs could elicit self- those maladaptive behaviors,and how the use of alternative improving behaviors. (Kiselica,1988, p. 303, 304.) "before", "during", and "after" stages. The following table shows theactions and thoughts in the (Kiselica, 1988, p. 305, 306.) TABLE 9 Examples of the Front and Back of a BDA Card Containing Self-Directed Questions and Answers for an Anger-Provoking Situation

Being Criticized by a Peer (Front of Card)

Before 1.What did someone else do before I became 1.Some guy criticized me. angry? 2.What was I thinking about before I became 2."That guy's trying to put me down ... angry? show the chump!" "I can't let other people see me get put down. So I'll show everyone how tough I am." During 1.What did I do once I became angry? 1.I threatened the guy. I punched the guy in his face. I cursed and yelled at the teacher when she broke up the fight. After 1.What happened to me or anyone else afterward?1.I received in-school suspension. The guy got hurt because I gave him a bloody nose. 2.How did I feel afterward? 2.I felt good at first because I proved how tough I am. Later, I felt bad because the kids at school think I am a bully. 3.What did I say to myself afterwards? 3."I showed the chump" (immediate thought). "I wish I could stay out of trouble" (later thought).

Being Criticized by a Peer (Back of Card)

Before 1.What can I say to myself to keep from getting 1."It isn't worth getting upset over ...I'll just angry when criticized by a peer? walk away." "Maybe the guy is really trying to help me instead of trying to put me down." "I want to have a good day so I won't let this upset me." During 1.What can I do instead of punching someone 1.Walk away. who criticizes me? Listen to the criticism and then discuss another subject. Ignore him. After 1.What happened to me or anyone else 1.I stayed out of trouble and nobody was hurt. afterwards? Received praise from the group home director 2.How did I feel afterwards? for having a good day. 3.What can I tell myself afterwards? 2.I felt good for not fighting. 3."I feel good . .I am having a good day!" "I did id"

59 7S All this information about cognitive psychology and counseling may be accurate, and even a little interesting, but does it relate to Jaime Escalante and what he does? The answer advanced here is a resounding "yes."Cognitive psychologists maintain that a person's cognitions, his beliefs, assumptions, and thoughts matter because they guide behavior and emotion. Clients who are having trouble coping and students who are doing poorly in school may have "faulty", "dysfunctional", "fictitious", or self-defeating beliefs, assumptions, and thoughts. It follows that one major goal of therapy or cognitive intervention is to"confront" or "attack" or "dispute" and "alter" those cognitions. Cognitive therapists work to change the client's "private views." Does Jaime do this? Does he work to change his students' private views? Does he attempt to change his students' beliefs, assumptions, and thoughts? Again the answer offered here is a resounding "yes."

Jaime doesn't just teach students to score high on ETS's advanced placement calculus test. He writes, "I have often said that I am trying to give my students two things, 'roots and wings . ..'I don't merely teach math, I teach respect for American democratic values and institutions...I often have the class salute the American flag.I teach the kids manners if they lack them . . . with these 'roots' firmly in place, they are morelikely to develop 'wings' to success, even greatness." (Escalante andDirmann, 1990, p. 11.)

Does Jaime restructure his students' cognitions? Does he alter their beliefs about what they can do? Does he give them 'wings'?" One needs only to read a few statements listed under the heading "Cognitive Restructuring" in Table 7 to find the answers.

He has helped me "set higher goals for myself in math" and "in life." He helps me "plan and strive for excellence." He has helped me see that "education is important," that "my first priority is to learn" andthat I should "put academics first." He helps me see myself as a "winner."

All of these statements can be seen as part of "a picture of the world" that Jaime isdeliberately presenting to his students. He writes,

"students can learn to overcome any barrier they will ever face ...I do not give up on my students and I expect them not togive up.. .the only thing you need for my programand you must bring it everydayis ganas (strong desire)."

"If motivated properly, any student can learn mathematics ...Often, I must persuade or cajole non-cooperative or frightened students into believing thatthey can do well with these subjects." (Escalante and Dirmann, 1990, pp. 3,4, 9, 12.) e

Over three years, Jaime continuously presents his viewsof the world and his students' potential for success. Like a good cognitive psychologisthe "disputes" self-defeating attitudes, "I can't do it; it's too d;fficult- and alters the way his students interpretthe world. "I can do it if I work hard and have the "'ganas'". "Education is important." If I try,through education, I can "become qualified for any job I want." Like a good cognitive counselor hedoes work to overcome false beliefs; like, "Severely disadvantaged, barrio students from the inner city cannotlearn advanced math; cannot achieve academic excellence." One of his main messages is,"You can do it, Johnny." "You can do it, Maria. Just watch me, I'll show you how."

Escalante's students may not believe they will die if they get water ontheir faces, but they and some adults around them may hold beliefs about the students potentialfor success academically and later in life that are far below what Escalante believes they canachieve. A big part of what he does is change the cognitions of his students so they more nearlymatch his own.

Escalante's students may be able to think ahead enough to realizethat the consequences will be too negative if "I punch him in the face and give him a bloody nose."But Escalante clearly works to help them think ahead and "understand that (by succeedingacademically in math and other subjects) I can become qualified for any job I want."

Additional evidence exists to suggest that Escalante's students havedeveloped an "I can do it" set of cognitions.Question number seventy-nine (#79) on the questionnaire tocalculus students (Appendix C) was meant to test "attribution theory." Thistheory asks, to what does a student attribute his success or failure. According to this theory, the causesof a student's success or failure are either "internal", to him (due tothe student's own ability and effort), or "external" tohim (due to the difficulty of the task and luck). In discussing attribution,the NEA booklet entitled, MQtivation: What Research Says to the Teacher put it this way. The research evidence in this field suggests that there are ways toincrease student motivation and achievement by teacher communicationand methods of instruction which help students make internal attributions(ability and effort) for success and lack-of-effort attributions for failure .. .Under these circumstances, students are less inclined to attribute success to external causes(luck, task difficulty) or to attribute failure to lack of ability (instead of lack ofeffort).

61 If students attribute successful learning to their ability and effort, they will experience pride and reward from their performance. However, if they attribute similar results to luck or task ease, they will feel far less positive. Also, if they attribute their failure in learning to a lack of effort which is changeable for future performance, they will experience some degree of hope and feel some control in their attempts at forthcoming similar tasks. In the same vein, if stut see effort as the key to success, perseverance will make a great deal more sense. But if students see failure as due to lack of ability, which is stable andmuch less open to modification, they will most likely experience far less hope and more feelings of incompetence and helplessness. And if students see a task as too difficult, they will not only expect failure to continue in similar situations, but the expectedfailure may also leave them with a chronic sense of frustration and anger .. . For teachers, this cognitive model implies that students are active participants in the learning process and the teachers' concern is not only to guide them and provide the best quality of instruction possible but also to enhance students' feelings of responsibility and personal control in the learning experience. (NEA, 1982, pp. 7, 10.)

To what do the students of Jaime Escalante attribute their success? In May 1991, fortyseven (47) of his calculus students and twenty-six (26) of his algebra 2 students chose their response tothe following questionnaire prompt: "#79. My success or failure in doing a math problem correctly is due mainly to. .." (see Appendix C.) The results are shown below in Table 10.

TABLE 10 Student Responses to the Prompt, "My Success or Failure in Doing a Math Problem Correctly is Due Mainly to ..."

Percent Res onse .0=11C1=1:21111111=CM:1111C a. my effort 30.1% b. my ability 11.0% c. my effort and ability 57.5% d. my good luck if I get it right, my bad uck if I get it wrong 4.1% e.the fact the the problem was either too easy, so I got it right; or too hard so I got it wrong 12.3%

1111111.

According to attribution theory, students who feel in "personal control oftheir learning experience"; that is, successful studentslike Jaime'sshould attribute their success to"internal factors" such as their own effort and ability. Thedata reported in Table 10 support this. About eighty-four percent (83.6 percent) of Jaime's students answered: a. "My effort," or b. "My ability," or c. "My effort and my ability"

This is exactly whi,is predicted by this cognitive theory.Students who are doing well academically should identify the cause(s) of their success asbeing "internal" to them (choices a, b, and c) not "external" to them (choices d ande).

"Teacher Expectations" is considered tobe a special subcategory under the"Cognitive Restructuring" heading. The main point hereis that teachers communicate what they expectfrom each student. That student in turn altershis behavior to conform more closely to histeacher's set of expectations. This self-fulfilling prophecyis sometimes also called the Pygmalioneffect, after the play by George Bernard Shaw. In themovie version, Eliza Doolittle (Audrey Hepburn)explains to Colonel Pickering. The difference between a lady and aflower girl ,s the way she is treated. I shall always be a flower girl to Professor Higginsbecause he always treats me as a flower girl, and always will; but I know I can be alady to you, because you treat me as a lady, and always will" (Ct-*ier Pictures)

More precisely, how do teacher expectationsaffect student performance ? Good andBrophy have idenlifies the following five-step process. 1. Tk teacher expects specific behaviorand achievement from particular students.

2.1,4'..-s3.use of these expectations, the teacherbehaves different, y towaK1 different .,,tedents. 3.Tois treatment by the teacher tells eachstudent what behavior and achievement the teacher expects from him orher and affects the student's self-concept, achievement, motivation, and level of aspiration.

4.If this teacher treatment is consistent overtime, and if the student does not actively resist or change it in some way,it will shape his or her achievementand behavior. High-expectation students willbe led to achieve at high levels, but the achievement of low-expectationstudents will decline.

5.With time, the student's achievementand behavior will conform more and more closely to what was originally expectedof him or her (Slavin, 1988, p. 377). Good and Brophy, after reviewing manystudies, found research support for the following tendencies:

...teachers respond more favorably to childrenfrom higher socioeconomic backgrounds, to girls, to high achievers, tocompliant and cooperative children, to attractive students, to those who sit in thefront and center sections of classrooms, and to those with neat handwriting andpleasant speech. They also concluded that almost all teachers seem to formexpectations about pupils after just a few daysof contact with them .. .(Biehler and Snowman, 1986, p. 534).

The lesson from research is that studentsdo (to some degree) live up to the expectationsthat their teachers express (directly or indirectly)for them (Slavin, 1988, p. 377). Doesthis apply to Escalante's students? Do they perceivethat he expects certain things from them?"Yes, of course" is the obvious answer. As shownin Table 7, there were seven expectationsthat his calculus students rated as more like him.

Does Jaime consciously use teacherexpectations to guide his students? Here areJaime's own words. economic status are expected to work ...When students of any race, ethnicity, or hard they will usually rise to the occasion,devote themselves to the task, and dothe work. If we expect kids to be losersthey will be losers; if we expect them tobe winners they will be winners. They rise, orfall, to the level of the expectations of those around them, especially their parentsand their teachers ...(Escalante and Dirmann, 1990, p. 9).

According to research done for thisguide, Escalante's students are well awarethat he has certain expectations of them. For example:

He expects "me to work hard" and "toachieve and do well in math." He expects me to be responsible; i.e.,he expects me "to attend class, come to class (xi time, and meet the assignmentdeadlines."

He expects me to be well mannered;i.e. he expects me "to be honest, courteous, and to show respect for others." He expects that "I can and will learn alot of math" and "will spend a lotof time on math". He "expects and rewards myacademic success."(See Table 7, "Teacher Expectations.")

64 Escalante mentions "hard work"frequently. For example, "The key to my success withminority youngsters is a very simpletime-honored tradition: hard work, and lots of it,for teacher and student alike." (Escalante and Dirmann,1990, p. 8.) The investigation to produce this guideasked for information directly related to hardwork, namely it asked students to fill in a blank toestimate the total number of hours per weekthey spent on homework for Mr. Escalante'sclass (see Appendix C, question #77). The averagefor seventy-three (73) respondents (47 calculusand 26 algebra 2 students) was 8.9 hours for just oneclass!

He expectsrequiresa great deal.In addition to the "ganas" students musthave, they are required to sign a contract, which amongother things, commits them to spending manyhours "doing math." Educational psychologistsrefer to this as "time on task." Students who enter the Escalante MathProgram must sign a contract which binds them to participate in the summer programsheld at ELAC, strict completion of daily homework and attendance at Saturday morningand after school study sessions. The students' parents are also required to signthe contract I sign it as well, obligating myself to bring ganas every day and todo everything possible to help the student succeed... One can find many of my students stillworking in my classroom (a convertedmusic hall) at 4:00, 5:00, or even 6:00 p.m. eachweekday and as early at 7:00 a.m. in the morning. No student with a question or aconfusion Ltd is allowed to go home with it unresolved. "Come after schooland see me at 3:00 p.m.," is the answerfor the student who is falling behind,who did not do his or her homework, orwho is having difficulty with that day's assignment(Escalante and Dimwit', 1990, p. 8).

65 Caveats

Every investigation in the behavioral sciences hasits limitations, this is no exception. Here are a few of the more obvious ones:

Time Sample Although the project was initially funded for three years,data from Jaime's colleagues and students were collected over about a fourteenmonth period. Student and colleague data were collected near the middle of the three year time frame, however and maystill be representative. Ideally, data would have been collected from students repeatedly; e.g., everyspring from all his Calculus A-B students.

Sample Sizes If Escalante's students had been questioned everyspring for three years, the sample size would have been 150 or more. This would have beensubstantial, and would have strengthened the student data.

Data from only two colleagues/key informants wereincluded. If more could have been located and had responded, the third leg of the "data source"triangle "would have been strengthened. But it was very difficult to findcolleagues of his who had actually observed him teachingfor any length of time. Others were asked.

Discussions were held with a science teacher and astudent worker, but neither returned the questionnaires. The science teacher admitted that hehad not had the opportunity to observe Jaime for any length of time, although he had, of course,worked with him Jaime and his project staff were protective of him andhis classroom. Occasionally, someone would begranted permission to observe--say for one day, but generally, outsiders were notinvited. In retrospect, this investigation was fortunate to have located two veryknowledgeable informants.

0 Questionnaires Two questionnaires were given, one duringthe pilot test to colleagues, the other to bothcolleagues and students. The first questionnaire wasbased on only one source, What Works:Research About Teaching and Learning. The second questionnaire wasbased on only four sources; i.e., two booklets, one journal article and the evaluator'sclassroom observation notes.

66 While a minimal number of sources formedthe basis for the second questionnaire, the two booklets were written as summaries of researchfindings taken from numerous studies found in the research literature. No doubt exists however, that everythingrelated to research did not become an item in the second questionnaire. That is to say, thequestionnaires were finite in length and the list of items covered was not exhaustive. Something was surelyleft out.

In addition, since there were several sources, itemstaken from one source may have been very similar to items taken from another. In short, there maybe overlap, so that items are not mutually exclusive.

Abbreviation To fit the questionnaire format, research findings werecondensed into short declarative statements. This shortening may have led to statements that wereincomplete or even inaccurate as compared to the original findings.

Response Rates Table 5 presents data based on responses of forty-seven(47) calculus students. The questionnaire (Appendix D) was given to students in two of Jaime'sCalculus AB classes. Given a typical class size of thirty-two (32), sixty-four (64) studentsreceived questionnaires.Consequently, the response rate for the Table 5analysis was 73 percent (47 + 64). Obviously,the higher the percentage the better, but 73 percent isbetter than might be expected given only thatalmost all the respondents (95 percent) were from an ethnic minorityknown to be at-risk. Appendix G presents data based on responses of seventy-three (73)students from three classes taught by Jamie: two classes of Calculus AB and one class of Algebra ILGiven a class size of thirty-two (32), ninety- six (96) students received questionnaires (AppendixD). Consequently, the response rate for the Appendix G analysis was 76 percent (73 + 96).Again, this is quite good, especially considering the at-risk status of the project students. Arbitrary Cutoff This Of the 75 items judged by Escalante's calculusstudents, 38 were said to be "more like him." involved rank ordering the scores given to each statement.But in talking about the top 38, and cutting the list into the top and bottom half it mustbe remembered that the choice of the midpoint as the cutoff was entirely arbitrary. Perhapsattention should have been focused ononly the top twenty statements instead of the top38. AmartntAssararaandOnisr In Table 5, seventy-five (75) statements about Jaime Escalanteand his teaching were rank ordered. Each of those statements were placed in the order shownbased on the mean (average) of scores assigned by a sample of forty-seven (47) of Jaime's calculus students. For example, the statement at the top of the listthe statement with a rank of #1was,"Mr. Escalante is funny or humorous." The mean of this top-ranked statement was 8.362. But the appearance of three decimal place accuracy and the order derived from it need to be examined. As we shall see,the accuracy and order, while true for the sample, are only approximate for a larger population.

Calculations were carried to three decimal places to produce a rank-ordered list with a minimum of ties. Even so, there are three ties in the top 38 statements. There are two statements with rank#7, two with rank #17, and two with rank #33. When ties occurred, the meansof those statements were exactly the same. For example, both statements, "Mr.Escalante is enthusiastic" and "Mr. Escalante is energetic" had means of 7.766 and both statements were ranked #7.

The next statement down the listwith a rank of #9"Mr. Escalante expects me to attendclass, come to class on time, and meet the assignment deadlines" has a meanof 7.761. This is only 0.005 below the mean of 7.766which we have already seen is the mean of both Mr. Escalante"is energetic" and "is enthusiastic." If one's purpose is to gener.alize beyond the sample of 47 to all of Jaime's calculus students, the difference of 0.005 must be seen as more apparent than real.When we go beyond the sample, we must talk not about adefinite point on a line; i.e., 7.761, but of an intervala range. In this case, the mean would change from 7.761for the sampleto a range that includes 7.761 as a midpoint

The mean for the population would become. 7.761 plus or minus a certain amount_This certain amount is due to error. In Table 5 the amount of error isshown for each statement under the column heading, "Standard Error" (the alpha level was set equal to 0.05).

Examples of surveys and interviews taken from recent headlines may behelpful. As the November 3, 1992, presidIndal election approached, numerous polls were conducted. Example 9ne. A YankelovichITimeiCNN telephonepoll of 958 registered voters axed the following question, "If the election for President wereheld today, for whom would you vote?" As of July 22-23, 1992, the results were, "53 percentfor Clinton and 26 percent for Bush." The report included the following additionalinformation, "Sampling error is plus (+) and minus (-) 3 percent." Thus, the percentage for Clintonin the totalpopulation of all registered voters in Americawas not exactly 53 percent (as in the sampleof 958), but rather 50-56 percent. Similarly, the percentage for Bushamong all registered voterswasnot 26 percent (as in the sample of 958), but rather 23-29 percent (Time,August 31, 1992, p. 14).

Example Two: Prior to Labor Day, the USATODAY newspaper and the Cable News Network (CNN) combined to support the Galluporganization's telephone survey of 1007 registered voters. As of August 31-September 2, 1992, the results were,"54 percent for Clinton and 39 percent for Bush." The USA TODAY article included the followingadditional information, "Margin of error: 3 percentage points." Thus, the percentagefor Clintonin the total population of all registered voters in Americawas not exactly 54 percent (as inthe sample of 1007), but rather 51-57 percent. Similarly, the percentage for Bushamong allregistered voterswas not 39 percent (as in the sample), but rather 36-42 percent. (USA TODAY,September 4-7, 1992, pp.1A., 8A.) It may be of interest to note that presidential surveyresults from Gallup over time and before LaborDay showed much less variation than those byYankelovich. As of July 18, 1992, Gallup reported the percentages as, approximately 55 percentfor Clinton and 33 percent for Bush.

In the first two examples, sample sizes wereapproximately 1,000; example one was based on a sample of 958, while example two was based on asample of 1,007. For both surveys the error was 3 percent As we shall seefrom the next two examples, as the size of thesample gets smaller, the size of the error gets bigger.

Example Three: For a Newsweek poll, theGallup organization interviewed 755 registered voters by telephone, October 8-9, 1992. Oneof the questions asked was, "Do you thinkClinton's anti- Vietnam war activities and his Soviet Uniontrip while he was a student at Oxford shouldbe an important issue in the campaign?" The results were,"24 percent 'yes' and 72 percent 'no." This time the margin of error was given as "plus(+) and minus (-) 4 percent" (Newsweek,October 19, 1992, p. 24.) As the size of the sampledropped from about 1000 to 755, the error went upfrom 3 to 4 percentage points. EnnuggEoja: For another Newsweek poll, the Gallup organizationtelephoned 433 registered voters after the first presidential debate onOctober 11, 1992. One of the questions asked was "Which candidate had the best answers on each of thefollowing issues?" Five issues were then listed. Here are the results for three:"Federal budget deficit:17 percent, Bush; 25 percent, Clinton; 49 percent, Perot.Ft) ,eign policy: 60 percent, Bush; 23 percent, Clinton; 11 percent, Perot.Health care:21 percent., Bush; 57 percent, Clinton; 14 percent,Perot." (Newsweek, October 19, 1992, p. 23.) As the size dropped to 433, the error increased to plus (+) and minus (-) 5 percentage points.

The point regarding the rank ordering in Table 5 is,if one wishes to generalize beyond the sample data (n=47), many of the means shown in the tablewould actually overlap. For the sample, the means and the order based on the meansin Table 5 is exact. The greater the generalization fromthe sample, the greater the error. If for example, we wished togeneralize from the sample of 47 to the total of 64 in Jaime's two spring Calculus AB classesthe error would be relatively small. On the other hand, if we wished to generalize from the sampleof 47 to all of Jaime's Calculus AB students 1989-1991, the error would be greater.In this latter case, for the population of all of Jaime's calculus students in the project from 1989-1991, theordering in Table 5 must be seen as only approximate. This is the main reason why, in this report, wehave spoken of the top thirty-eight statements as being "more like Mr. Escalanteand his teaching" and the bottom thirty-eight as being "less like Mr. Escalante and his teaching." It must benoted that in the middle of the listwhere an arbitrary cutoff was madethere is no doubt thatthere is some overlap. The column "Standard Error" in Table 5 shows how much error and how muchoverlap there is when one wishes to generalize to the greatest degree possible.

To illustrate how the overlap works when onegeneralizes the most, let us consider both the top- ranked and bottom ranked statements in Table 5. The top statementin this list, the one with the highest mean (8.362) and rank #1, actually overlapswith the next four statements down the list. This is so since the bottom of the interval forthe top statement is 8.178 (8.362.184), andthis overlaps with the top of the interval for the rank #5 statement,8.229 (7.957 + .272). The bottom of the interval for the rank #1 statement(8.178) does not overlap with the top of the rank#6 statement (8.151=7.891 + .260) since8.151 is less than 8.178.

70 The bottom statement in this list, the one with the lowest mean (1.674) andrank #75, overlaps with only the one just above it, the one ranked #74. This is so since the top of the interval for the rank #75 statement (2.516 = 1.674 + .842) overlaps with the bottom of the interval for the rank #74 statement (2.306 = 2.872 - .566) but does not overlap with the rank #73 statement which has a top interval boundary of 2.599 (3.234 - .635).

Cearly, while there is overlap within the table, extremes of this list do not overlap. The bottom boundary of the rank #1 statement is 8.178 (8.362 - .184), whereas the top boundary of the rank #75 statement is 2.516 (1.674 + .842).

Again, remember that if one does not generalize beyond the 47 respondents, the figures inTable 5 are exact and there is no overlap. Further, if one generalizesonly to the 64 students in Jaime's two spring '90 Calculus AB classes, the overlap would be slight. And, as we've just seen,if one generalizes as far as possible, there is overlap within the table but not between those statements near the top and those near the bottom.

Finally, after all these cautionary statements, it should also be noted that informationgathered properly by a questionnaire or survey can be quite accurate.Let's continue to use data from polls and compare the actual vote on November 4, 1992, to the results of six pollsconducted through November 1, 1992 (USA Today, November 5, 1992, p. 6A). Remember that more than100 million Americans actually voted.

Table 11 How the National Polls Fared

Candidate poll Clinton BushPerot Actual vote 43% 38% 19%

The Harris Poll 44% 38% 17% ABC News 44% 37% 16% NBCfWall Street Journal' 44% 36% 15% CBS/New Yc.lc Tunes' 44% 35% 15% 'Washington Post' 43% 35% 16% USA TODAY/CNN/Gallup 49% 37% 14%

71 In the popular vote, Clinton actually won by five percent (5% = 43%-38%). The Harris Poll came the closest, predicting his win by six percent. All polls correctly predicted Clinton to be the winner and next president.

Omitted Item In "Part 4: Interview with Jaime Escalante" the intent was to ask him to react to the topthirty-eight (38) statements rated by his calculus students as more like him (Table 5). He graciously did respond to all statements read to him. However, through no fault of Mr. Escalante, the interviewer mistakenly omitted the 11th ranked statement, "Mr. Escalante expects that I can and will learn a lot of math." Fortunately, this statement is somewhat similar to two other statements to which he did respond, "expects me to achieve and do well in math (rank #2)" and "gives me a lot of math problems to do (rank #20)." (See Table 5.)

Scale of Measurement The rating scale (from -9 through +9) used by Mr. Escalante's Calculus studentsanddisplayed in Appendix Dis assumed to be a ratio scale.

Political Ideology Is "What Works..." a political document? At least one writer thinks it is. Gene Glassis a professor of education, Division of Leadership and Policy Studies at Arizona State Universityin Tempe, Arizona. In April 1987, an article of his was published in the journal, "EducationalResearcher." It was entitled, "What Works: Politics and Res)earch."(Glass, 1987.) In that article, he argued that "'What Works...' is an expression of historical American conservative political philosophy."He asserted that "conservative favorites are quoted more often or to the exclusion of liberalthinkers. One listens as Plato the moralist speaks, while Aristotle the democrat and empiricistis silent" (Glass, 1987, p.7).

Having read the first edition of "What Works..." published in January 1986,Glass noted that a number of important findings were missing. His list of omissions included:

Open education is superior to traditional education in fostering students' adjustment, attitude toward school, creativity and independence (Giacona& Hedges, 1982, pp. 579ff, based on roughly 20 studies);

Cooperative learning is superior to competitive learning (Johnson, Johnson, & Maruyama, 1983, based on 100 studies);

72 Computer Assisted Instruction (CM)benefits students. (Levin, Glass, and Meister, 1987, based on 300 studies);

Children learn more in smaller classes (Glass,Callen, Smith, & Filby, 1982, based on 77 studies) (Glass, 1987, p.7).

A reader of the Glass article might note thatGlass himself had obviously done research or reviewed research in at least two of the areas he claimed shouldhave been included in "What Works... ." His name as author appears twicein his list of omitted findings. (See above.) Itshould also be noted that Glass used the first edition of"Whit Works..." whereas this Instructional Guide used the second edition which included 18 more researchfindings.

Still, his point that the political ideology of theReagan administration influenced the developmentof "What Works..." should be considered. Afterall, "What Works..." was created during theReagan administration and under the supervision of Reagan'sappointee, William Bennett. And, Reagan and Bennett declared themselves to bepolitically conservative.

Glass further asserted:

The political goals of "What Works..."are thoseof the administration that produced it: To disestablish the federal bureaucracyin education, to decen- tralize control over education, to deregulatethe practice of schooling, and to diminish financial support for schools (Glass,1987, p.8).

Finally, Glass concluded that "What Works..."...is mirabile dicta, a political document...(that it invokes research) in a modem ritual seekinglegitimation of the Reagan administration'spolicies." "What Works..." does this and,. lest oneforget, previous administrations havedone the same" (Glass, 1987, p.9).

73 A number of statements by Glass seem to ring true. For example, he states, "The findings favored by its ("What Works...") compilers are those that seem to cost nothing" (Glass, 1987, p.8). Glass could be right. Findings like: "expects me to work hard (ranked 4th)," "gives me a lot of math problems to do (ranked 20th)," "expects me to attend class, come to class on time, and meet the assignment deadlines (ranked 9th)," and "expects me to be honest, courteous, and to show respect for others (ranked 13th)" (see Table 5) do appear to call for no additional financial support from the federal government. This would be in line with Glass' assertion that politically conservative goals would include reducing financial support for schools. Apparently, Glass would say that this is why these findings were included, whereas the finding, "Children learn more in smaller classes" (Glass' list) was excluded. Reducing class size would be costly, and violate the conservative political philosophy.

But, even if Glass were 100 percent correct in his assertion that "What Works..." is highly political, it is difficult to see how that would reduce the usefulness of "What Works..." in the development of this instrnctional Guide. In civil law there is a pleading called a "demurrer." After the plaintiff has formally filed his suit in which he has presented his arguments, the defendant may demur. That is, he may file a demurrer in which he assumes as true the matter as alleged by the plaintiff, and then argues that even if all of the allegations were true it would be insufficient toconstitute a legal reason why the defendant should not be allowed to proceed further (Webster's New Collegiate Dictionary, 1973).

For example, let us assumeas Glass assertsthat findings about: "open education," "cooperative learning," "computer assisted instruction," and "putting students in smaller classes" should be included in "What Works... ." Even if these had been contained there, one would have to recognize that none of these apply to Jaime Escalante and his teaching. In fact, relative to class size, quite the opposite is true. Thirty-two students is certainly not "small" for a calculus class and yet Jaimehad at least that many. And, there were easily twice that number (64)in his summer trig-math analysis class. Further, he did not use computer-assisted instruction or any of the other practicesin the above list by Glass. In summary, the findings which Glass states should havebeen added would not have contributed toward the development of this InstructionalGuide. Their absence had no impact.

Glass reports that secretary Bennett, in an early memo to his staff"enunciated his 'three Cs' of education: Character, content, and choice" (Glass, 1987, p.9). Glassdescribed some members of congress as angry over how Bennett had spentdiscretionary research monies"Too much concern for research on character development and vouchers..." (Glass, 1987,p.8).

74 A number of findingsrelated to character development did find their way into "What Works..." and some wereranked by Escalante's calculus students as very much like him andhis teaching. A partial list would probably include thefollowing: "expects me to work hard," "gives me a lot of math problems to do," "expects me toattend class, come to class on time, and meet assignment deadlines," and "expects me to be honest, courteous,and to show respect for others." (See Table 5.)

Even if, as Glass asserts, findings like these are partof character development and therefore part of a poll ically conservativeideology, does that make any difference as far asthe Instructional Guide is concerned? Probably not.

'Jaime's students were given these instructions:

It seems extremely doubtful that, as they werefilling in their ratings, students took into account whether or not statements represented a politically liberal orconservative position.

In summary, the factif it is indeed afactthat a statement arose from a given politicalposition probably had no effect on the students' ratingspresented in this Instructional Guide.Furthermore, the additional findings suggested byGlass simply do not apply to the tasks ofthis Instructional Guide; namely, to identify and describe theteaching and motivating practices of JaimeEscalante. Important findings may have been excluded, ashas already been noted in this section.

Glass' contribution is that he has pointed outthat a number of those missing findings mayfit within a political philosophyin conflict with the Reagan/Bennett versionof political conservatism.

75 Investigator's Point of View While every attempt was made tobe as objective as possible and presentthe results of questionnaires and Jaime's interview in a"They said this" and "He said that" format,the point of view of the one conducting the studyand doing the writing is a factor that mustbe recognized. In the Discussion section of this paper,especially where an effort was made tosimplify the data, the point of view of the investigator isof obvious influence. Seeing similaritiesbetween what Mr. Escalante does and "cognitiverestructuring"for example, reveals the writer'sinterest and background as well as state credentialsand licenses in counseling andpsychology. Some other writer, upon seeing the same resultswould probably call it something else;such as "instilling a vision," or "giving them wings."

Concerns About Validity

The term validity is defined as thedegree to which a test measures what itis supposed to measure accurate, are (Biehler and Snowman, 186, p. 147).The question here is, "How valid, e.g., true or the findings presented in this report?"Do the thirty-eight statements hiscalculus students identified as more like him trulyand accurately describe him and hispracii,--s?

impaneled to make those A In the legal system, where thetruth about events is in dispute, juries are judgments. Here, in the absence ofobjective truth, both categories ofparticipants the teacher and the studentswere questioned. In a mannerunique to this study, students wereasked first and the interview. with Jaime teacher later asked whether he agreed ordisagreed. Throughout Part 4the Escalante the teacher had ampleopportunity to disagree with one or allof those statements. Mr. Escalante--who readily speaks hismindclearly accepted the statementsidentified by his calculus students. As jury members vote ontruth, here Jaime and his studentsvoted on teacher attributes the validity and practices. In short, Part 4 offers a validitycheck by the master teacher himself as to delete or truth or accuracyof the statements identified earlier.He did add to those, but he did not any. (See Part4.)

used. The three data In this guide, the qualitativeevaluation procedure of data triangulation was colleagues, and Escalante himself.The sources were:Escalante's calculus students, Escalante's third point on the "data triangle"- - statement ranking done byhis colleagues/key informantsthe calculus students. In fact, of the produced a ranking very similar tothat produced by Escalante's thirty-eight statements rated by students as morelike him, key informantsidentified twenty-eight (74 percent) of those (see Table6).

76 Is there support for the notion that the statements wereranked accurately? A fourth source of informationthe journal article can be consulted. Although an exhaustive analysiswill not be offered here, the following may be of interest.

His calculus students put this statement at the top of their list,"Mr. Escalante is often funny or humorous." (See Table 5.) In the interview in Part 4 of this paper Mr.Escalante agreed that he intentionally uses humor as a teaching/motivating practice. Furthermore,in the journal article under "Teaching Methods, Humor" he wrote: I learned early in my career that teaching is funat least, itshould be fun. Students learn better when they are having a good time. While I teach respectand discipline and I demand a great deal of hard work from my students, Ialways try to do it in a way that is fun. I use toys, tell lotsof jokes, and let the kids participate. A teacher must enjoy his or her work and convey that joy tothe students. I have found that humor carries ideas much better than a grave monotonebecause it makes its recipients far more willing to receive what the teacherhas to say. In fact, I have heard that some students enroll in my program justbecause they heard it was fun, despite having little initial interest in mathematics. Thatdoes not bother me, howeverusually, the interest will follow. (Escalante and Dirmann,1990, p.7)

His calculus students certainly picked up on his intentional useof humor. Furthermore, in their essays on Escalante, both key informantsmentioned his "humor" or "wit."

His students put this statement at thebottom of their list, "Mr. Escalante encourages me to get involved in extracurricular activities to round out my education."(See Table 5.) In the journal article he wrote:

I admit that I am jealous of my students' time andthe distractions which compete with my math program. I discourage them from fillingtheir schedules with TV, sports, or other forms of "goofingoff." I chide them for the headsets which pipe strains of "heavy metal" guitars into their ears whenthey should be working on math. I play good "defense" for my program, too.When I have to tackle aspiring athletes who want to drop calculus so that they can go tofootball or marching band practice, my argument is simple: In the 16 years thatI have been at Garfield, not one graduate has gone on tomake a living playing football, basketball, orbaseball.. .From where I sit, however, I know that takingAP Calculus has a lot more to dc with my students' future success than any ball or baton astudent will ever pick up. (Escalante and Dirmann, 1990, p.9)

77 9 6 Again, his calculus students seem to haveunderstood him perfectly. He "believes my first priority is to learn (not play sports, etc.)" and he "putsacademics first." These are the second and third statements in the student's list (Table 5).It is clear that Escalante does not encourage his students to get involved in extracurricular activities.This item should be at the bottom of the list because itis very unlike him.

There are numerous other examples one could identify thatshow a consistency between what Mr. Escalante has written and what his students report theyexperience.

Q 78 Conclusion

The purpose of this report was to document"...the body of techniques that make up the teaching and motivating methods of Jaime Escalante."(ELAC, 1988, p. 21.) Opinions were solicited from key informants, knowledgeable colleagues of hiswho had observed him for years; and his calculus students, who had taken math classes from himfor three of four years. To verify the opinions of his calculus students, Mr. Escalante himself wasinterviewed and asked whether he used the thirty- eight practices identified by them as more like him.Knowledgeable colleagues also responded.

The insights into this exceptional teacher's practices are notpresented here as conclusive or all inclusive. When this investigation was launched, no oneexpected Mr. Esca;.a.-ite to leave Garfield High School and East Los Angeles College and the MathProject to go to Sacramento where he now teaches at Hiram Johnson High School.This investigation, therefore, was meant to be developmental; that is, to be a first step toward a morecomplete explanation. After he left, it seemed that this report and this investigation wouldneed to stand alone, without additional data gathering and analysis.

But fortunately, as the project moved into the last summer(1991) in which L3calante was a teacher, a videotape was made of himteaching his trig/math analysis class. Even if he never returns toteach in southern California, the project has this tape that canbe analyzed in the future. This is as close as the project came to obtaining an objective record.

Now in Sacramento, Escalante is involved in producing aseries of "demonstration lesSons." While these lessons will no doubt prove very useful inteacher and administrator preservice and inservice training, their usefulness in research is reduced by thefact that those actions are being done for the camera to make a profit.In contrast, the videotape held by themath project was done as unobtrusively as possible during a real class (trig/mathanalysis) with real students. The classroom behaviors captured on tape by the project wereunrehearsed and involved real students, not actors. For these and other reasons, the project tapeasthe more unobtrusive and objectiverecord--is much more prized for its future researchpossibilities. A number of outstanding evaluators are interested in the tape. At the 1990American Evaluation Association Conference in Washington, D.C, when parts of this guide were presented, two very highly thought of researchers attended, Dr Daniel Stufflebeam and Dr. Michael Scriven. Dr. Stufflebeam is now the Director of the Center for Research on Educational Accountability and Teacher Evaluation located on the campus of Western Michigan University. Dr. Scriven is the Director of the Evaluation Institute of the Pacific Graduate School of Psychology. Both are evaluators with an international reputation. This tape may well be the last, best hope as a primary source for a series of very detailed studies on this exceptional teacher'seffectiveness.

Certainly, further research should be done using the Escalante trig/math analysis tape. In addition, more detailed comparisons could be made between thejournal article and the judgments made by Escalante's colleagues and his calculus students. As noted in Appendix A, Escalante's colleagues provided more information than was presented in Part 2; each wrote an essay, for example. Allthis deserves further attention.

For now, this paper provides the multiple perspectives of key informants, Escalante's calculus students, and Escalante himself. These perspectives have, for the most part, beenrelated to research findings that describe effective practices. Surely, who Mr. Escalante is and whathe does is much too important to be seen from one perspective only.

Fortunately for the students at Garfield and Roosevelt High Schools, the agencies that fundedthe original Escalante Math Project for three years, 1989-1991, have seen fit to continuetheir support.

Nssible Replication of the_ Program It would be nice if America had an army of at least a thousand Jaime Escalanteswho could go into barrio high schools all over America, reverse the high dropout rate and leadthose inner city high school students to academic excellence. But, of course, the truth is, wedon't have a thousand Jaimes; and given the fact that he is 61 years old, America may not havehim as a full-time math teacher for very much longer.

80 (40 Several questions arise. Can the original EscalanteMath Project based at East Los Angeles College continue to be successful without him? Could the programbe repeated elsewhere? Jaime has given his answer: I have described the elements of my program. I believe thatthey can be duplicated elsewhere with ease. The key for the teacher as well as for thestudent is hard work. Hard work makes the future. When hard work is combinedwith love, humor, and a recognition of the gangs the desire to learn, the ability tosacrifice, the wish to get aheadthat burns in our young people, the stereotypes andthe barriers begin to crumble...I always have to laugh when someone suggests that my programis dependent upon one teacher's personality ( .iy own) andcould never serve as a model for use in other schools. It just shows how far away wehave drifted from the fundamentals of teaching (Escalante and Dirman,1990, pp. 6, 14).

8 1 I) References Benedetto, Richard. (September 4-7, 1992). Poll: Bush Loses Bounce: 15-Point Gap Could Turn on Economy Issue. USA Today, pp. 1A, 8A.

Biehler, Robert F. and Jack Snowman. (1986). Psychology Applied to Teaching. Boston: Houghton Mifflin Company.

Blakely-Saba, Peter, Ira, Wyman; Downing, Larry; et al. (October 19, 1992). "Face to Face to Face on the Debates: Round One." Newsweek 120, 16:20-24.

"Can This Man Save American Education?" (April 1990). Connoisseur 220, 5:88.

Christian, James L. (1973). Philosophy: An Introduction to the Art of Wondering. San Francisco. Rinehart Press.

Corsini, Raymond J. (Ed.) (1984). Encyclopedia of Psychology. New York. John Wiley and Sons.

Denzin, Norman K. (1978b). The Research Act: A theoretical Introduction to Sociological Methods. New York: McGraw-Hill.

Fielding, Nigel G. and Jane L. Fielding. (1986). linking Data Qualitative Research Methods Series No. 4. Newbury Park, CA: Sage Publications.

Glass, Gene V. (April 1987). "What Works: Politics and Research." Educational Researcher 16, 3:5-10.

Gumaer, Jim and Tanya Headspeth. (May 1985). "Self-Instructional Training with an Adolescent Schizophrenic." The School Counselor: 32, 5:371-380.

Hubbard, Kim. (April 11, 1988). "Beating Long Odds, Jaime Escalante Stands and Delivers, Helping to Save a Faltering High School." People 29, 2:57.

Kantrowitz, Barbara, and Lourdes Rosado. (August 19, 1991). "Falling Further Behind: A Generation of Hispanics Isn't Making the Grade." Newsweek: 60. Kiselica, Mark S. (March 1988). "Helping an AggressiveAdolescent Through the 'Before, During, and After Program'." The School Counselor:35, 4:299-306.

Kroll, Jack. (March 14, 1988). "Stand andDeliver (movie review)." Newsweek 111, 1:62.

Mathews, Jay. (1988). Escalante: The Best Teacher inAmerica. New York: Henry Holt and Company.

Mathews, Jay. (January 1989). "Miracle Worker of Garfield High."(Excerpt from Escalante: The Best Teacher in America.) Readers Digest 134,30:165-202.

Mathews, Jay. (July 20, 1992). "Escalante Still Standsand Delivers." Newsweek 120, 3:58-59.

McGrath, Ellie (December 27, 1982): "Low-tech Teaching Blues:Crisis in the Math and Science Classrooms." Time 120, 1:67.

Meek, Anne. (February 1989). "On Creating 'Ganas': AConversation with Jaime Escalante." Educational Leadership 46, 5:46-47.

National Education Association. (1986). Motivation: WhatResearch Says to The Teacher. (rev. ed.). Washington, D.C.: NEA Professional Library.

National Education Association. (1990). The JaimeEscalante Math Project. Washington, D.C.: NEA, (Reprinted from the Journal of Negro Education, summer1990, 59, 3.)

Norman, Jim. (November 5, 1992). Undecideds, PerotThrew off Pollsters. USA Today, p.6A.

Patton, MichaeL (1990). Qualitative Evaluationand Research Methods. (2nd ed.). Newbury Park, Ca: Sage Publications.

Savage, David. (spring 1986). "Don't Tell JaimeEscalante Minorities Can't Meet (High) Standards." Instructor (California Special Issue)30, 4.

Slavin, Robert E. (1988). Educational Psychology:Theory into Practice. Englewood Cliffs,N.J. Prentice HO.

83 Staff. (August 31, 1992). The Week: Nation: Playingfor the Big Bounce. New York, N.Y. Time 140, 9:14.

U.S. Department of Eduction. (1987). What Works:Research About Teaching and Learning. (2nd ed.). Washington D.C.: U.S. Governmentprinting office.

Webster's New Collegiate Dictionary. (1973). Springfield,Massachusetts: G. and C. Merriam Company.

Woo, Elaine. (June 14, 1991). Math Teacher EscalanteQuitting Garfield High. The Los Angeles Times, pp. Bl, B4. Appendix A The Jaime Escalante Math Project Item 1 Project Description

The Jaime Escalante Math Program involves manyelements that research has shown are characteristic of highly successful programs: a comprehensivewell-developed plan, dedicated staff, parental involvement, community support, motivationalstrategies, agreed upon objectives, and coordinated support services. This program prepares inner-cityunderrepresented students for the Advanced Placement Test in calculus, computer science,chemistry, English, and physics. On the face of it, the Escalante strategy is quite simple. Extrapractice after school and during Saturday sessions builds student confidence. Each success leads tohigher goal setting and the willingness to take on extra work.

The Jaime Escalante Math Program annually provides500 elementary, middle school and high school students with hands-on practice to supplementdaily instruction. These sessions occur regularly after school, on Saturdays during the academic yearand for six weep during the summer. Students in the program are from families with amedian income of less than $16,000 and an average family size of five. Ethnicallystudents identify themselves as Hispanic: 91.7 percentwhile 1.1 percent are white. Most parents have notcompleted high school (58 percent).

The Saturday component, a four hour session,conducted at East Los Angeles College, is primarily a review of the work covered during the weekwith an opportunity for added practice.

During the summer, students are enrolled for anintensive six week session during which participants complete a full year of math instruction.Classes, from 8:00 a.m. to 12 noon, include Algebra lAB, Algebra 2AB, geometry,trigonometry, and mathematical analysis. Afternoon sessions, from 1:00 p.m. to 4:00 p.m., includeoptional sessions in physics, computer science, and preparation for the verbal (English) portion ofthe Scholastic Aptitude Test. Friday is testday, generally the first two hours. The remaining twohours are used for group and individualacademic and career counseling, guest lecturers fromindustry or university, and tutoring. Collegereadiness and vocational interest testing is provided.Fridays often include field trips to localuniversities and recreational trips to local beaches and parks. Appendix A (continued)

College students who are interested in careers as mathand science teachers are used extensively throughout the program, during class sessions,after classes and on Saturdays. A tutorial component is offered from 3:00 p.m. to 5:00 p.m.,Monday through Friday at the local school campuses. The program serves students who arein pre-algebra, geometry, Algebra 1AB, 2AB, math analysis, trigonometry, and in preparation for the APexamination.

Breakfast and lunch in the college cafeteria is provided on Saturdaysand throughout the summer (subsidized by the U.S. Departmentof Agriculture). Participants who qualify (low family income are provided 25 hours per week of paid work on campus orin the community. All work experience stipends are funded through the Department of Labor(ITPA) and go directly to the students.

Additionally, the design of this program includes a variety ofintervention and preventive strategies to address the special needs of the educationallydisadvantaged, at-risk students from low income communities. In summary, the instructional programinvolves an intensive summer program and academic year Saturday programthat has the following components:

1. Summer Program - Summer Programs will include basicacademic instruction and cultural enrichment activities for 500 inner city, minoritystudents. 2. Saturday School - To support the gains made during theintensive summer program students will attend a specially designed Saturday program29 times an academic year. 3. Afternoon Tutoring - To reinforce the day's instructionand to keep11 students current, the high school and junior high schoolteachers are available, along with tutors, fimm 3:00 p.m. to 5:00 p.m.Mondays through Thursdays, fall and spring. 4. Peer Tutoring - Peer tutoring will be available duringthe summer programs, Saturday sessions, and afternoons, fall and spring. Successfulstudents interested in careers as math teachers will be trained to provide peer tutoringfor high school students. 5. Parental Involvement - Parental involvement is essential tostudent's success. This project will support a variety of strategies that have beeneffective in creating a climate of parental involvement. Appendix A (continued)

6. In-service - Extensive in-service will be provided to teachers, counselors, and parents to develop the expertise needed for a high quality, model program.Program staff will enhance their capabilities to assess student progress and adapt instruction toindividual needs. New, pervasive motivational strategies will be reviewed.Parents and counselors will receive training to understand the special needsof the target population. 7. Curricular Development - This project will involve original, comprehensive,well planned, systematiC, and carefully constructed curricula sensitive to theunique needs of these students. Teachers manuals, curriculum materials, and lessonguides will be developed for use by program staff. 8. Intersegmental cooperation - This program will bring together teachers,counselors, and staff from junior high schools, high schools, community colleges,and four year colleges to improve course articulation and to better address the uniqueneeds of the target population. 9. Corporate Partnership - This project will help these students toexplore the linkages between school and work.In cooperation with our corporate sponsors we will undertake mock interviews, corporate mentors, career guidanceworkshops, work experience options, and tours of work sites.

87 1. 1)6 APPENDIX A The Jaime Escalante Math Project Item 2 Project Teachers and Staff 00

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89 Appendix B Questions to Key Informants

After a meeting with Dr. Kester, keyinformants were given: 1) The booklet entitled "WhatWorks: Research Aboil Teaching andLearning," 2) An open-ended question, and 3) A Questionnaire.

The open-ended question was:

In your own words, based onwhat you know, what are someof the important factors that account for Mr. Escalante'steaching success?

The questionnaire began with a coversheet that presented the following:

Sisal; To describe the intersection ofSet A and Set B (A n B).

Given: Set A = {The Successful Teaching andMotivating Practices of Mr. Jaime Escalante) Set B = {The researched practices brieflydescribed in the booklet entitled, "What Works..." Research practices, are contained within Ouestion: What elements; i.e., successful both Set A And Set B?

The questionnaire was entitled:

Teaching Practices: Getting A Pilot Project to IdentifyJaime Escalante's Successful Started Conceptually by Using theResearch Foundation in "What`iv orks..."

contained all fifty-nine The first column of the questionnaire wasentitled "Research Findings" and headings contained questions tobe research findings taken from"What Works...." Other column answered.

Column #1 Research Findings Appendix B (continued) column #2 Judgment Call Question: Does this research finding to some extentexplain the teaching success of Jaime Escalante? Please put a check next to the best response.

Yes, a great deal Yes, for the most part Somewhat Only a little No, not at all

Column #3 Examples Questions: Can you think of one or more real life examplesof this research finding in action in his class? What happened? What did hedo, say c: require from the students? How did the students respond? If you canthink of examples, please write some words or phrases that at least begin to describe thoseexamples here.

Column #4 Meaningful Words or Phrases Question: Even if the research finding does notapply, there may be some meaningful words or phrases that we could later use to construct our ownsentence that would describe his teaching success. Are there any such words orphrases in either the research finding itself or its comment section that we couldlater use in this way? If so, please write those words or phrases in this column.

Column #5 Other Question: Do you have any additional ideasrelated to this research finding or its comments section? If so, please write those ideashere.

The key informants also completed thequestionnaire shown in Appendix C. Twenty Eight Research Findings Identified by Key Informants The Last Tier Table C-1 1. Curriculum of the Homo As Least Helpful in Explaining The Teaching Success Of Jaime 11. Teaching Writing 21. Mainstreaming Escalante academicchildrenWhatand"Parents most parents learn aresuccess influential their is domore than children's to how importanthelp well-off their first to teachers. ofwriting"The revising,brainstorming, most is to effectiveand teach editing" it composing, wayas a(p. toprocess 31). teach physicallyinbeemotional"Many well-supportedgiven anhandicapped or appropriatelearning regular problems or education haveclasses can children who are 2. Readingthe family to r,jairfin is" (p. 5). 12. Vocabulary Instruction "Students22. Cultural read Literacy more fluently and withand schools" ( p. 69). eb areistheir"The fromto very readchildren best readingyoung. toway them become for aloudeven parents better when when toreaders helpthey they Children benefit experiencesarebetter"Childrenthey when already the and possess" words to knowledge they (p. 33). study related learn to vocabulary familiar culturalknowledgeculture,greater literacy"understanding past and of andunderstanding the (p. present.71).world if theyand is calledtheirhave Such n 3. ladeptadentileadingmeaninglettersdiscuss and ofstories, words,words" learnand(p. 7). talk to aboutidentify the 13. Reading Aloud 23. reign Language schooltheachievementability"Children amount and by outside" readingofimprove readingis directly (p.a their lot. children8). related reading do into Reading encouraging36).themto"Hearing read become a good passagestudents good readers aloudrepeatedly readers" read helps and (p. manyandlanguage"The to years"best study in way school(p. it 73). tointensively learn is to starta foreign earlyover 1 4 Si Table C-1 4. Early Writing 14. Student Ability and Effort (continued) 24. School to Work Transition earlydraw"Childrenmore age and easily, will whoscribble later moreare learn encouraged'stories' effectively, to compose at anto and grow"andrelationship"Children's hard (p. 37). work understandingbetween changes being as ofsmart they the whenlikelystudents"Handicapped toschools findwho jobs seek prepare after them graduation themare more for high school 5. Speakingencofchildrenwith tragement" and who Listening (p.do 9). not have this greater confidence than 15. Purposeful Writing 25. History, businessescareerstraining" (p. provide 76). on-the-job and private sector betterlistening"A good readers" foundation helps (p. children 12). in speaking become and goalstheretheirin"Students writing forwritingare writing become significant and improves assignmentsthe more quality learninginterested when and of inclassesdeclining"Skimpy (p.students' 77). are enrollmentscontributing knowledge ofto in thea history decline past" requirements and 6. Television"Excessive television viewing is 16. Libraries a clear"Thewriting" usesense (p. of 43). librariesof purpose enhances for 26. Accelealklia "Advancing gifted students at a achievement.associated13).parents,especially can with whenhelp low children supervised academic learn" by(p. Moderate viewing independentreading skills learning" and encourages (p. 60). giftedachievingnormalfaster students rate" more (p.78).who than are taughtsimilarly at a pace results in their 40 (contint led)Table C-1. 7. "ParentalGetting Parents Involved involvement helps 17. Succeeding In a New School "When schools provide 27. Extracurricular Activities "High school students who Teacherschildrentheyschoolworkinvolving work learn who parentsat areit" moreare (p.successful in successful17). effectively.their children's because at fromprogramscomprehensiveadjustmentease one the forschool special students difficulties to another, stressestransferring they those and orientation gainwithcomplementtheir experience extracurricular success their in that college"academic contributes (p. studies 79). to activities 8. 18. Instructional Support (p.bestudents improved65). face. student The result performance" is apt to 28. Work Experience 1/40 Phonic2 or mildly "When students work more than 15 A "ChildrenlettersunderstandLearningreading and if get theyphonicssoundsthe arelationship are better and taughthelps to start 'break phonics.thembetween in theto arewhenmosthandicappedUnderachievingthose closely thefrom in lessons their remedial coordinaialstudent regulia in *close can.education classes" benefitclasses with (p. schoolhowever,mayto 20 suffer.hours work" from per (p. week,80). limited their out-of- grades They can benefit, 9. BeadinfiSsmxihswilenwithcode'19). the that words links theythe words see in theyprint" hear (p. 19. Collegiality 66). precedesassignment"Childrendiscussion"information the get lesson (p. morewhen and20). with out followsthe ofbackground a reading it with teacher growth"onecooperatewhen"Students their (p. inbenefit teachers67). activities, academically share and ideas, assist another's intellectual 10. Storytelling 20. Teacher Supervision (continued)Table C-1 valuesalsomotivate"Telling introduces and young them literary tochildren themread. traditions Storytellingto cultural before stories can work,suggestions"Teachersthem" but (p. welcome theyabout68). rarelyimproving professional receive their DepartmentNote: All research of Education, findings were takenstoriesthey can by read, themselves" write, (p. 23). and talk1987. about Page numbers in parenthesis from What Works. Research on Teaching refer to this publication. and Learning, Second Edition, published by the United States

1 Appendix D Questionnaire to Escalante's Calculus Students The Escalante Mathematics, Science & Computer Science Project

Name Sex:Male Female Address City Zip Date of Birth, / Social Sec. No. The name of the class I'm taking that Mr. Escalante teaches is This class meets during period # <<<<<<<<<<<<<<<<<<<<<<<<<<<<<< <<<>>> > >>>> >> > >>> > >>> > >>>>> >>>>

Instructions As you know, Mr. Escalante's success in helping students learn math has broughtwell deserved national attention to his students, to him, and to Garfield High School. When you answer thefollowing questions, you will be helping us better un- lastand why you, hisstudents, are consistently successful in math and why he is an exceptional teacher. Your cooperation is voluntary, and answering eachquestion is at your option. We want you to know that the individual information you provide will be held in the strictestconfidence and will be used in aggregated form for research purposes'only. Thank you very muchfor your cooperation.

Below are seventy-five statements that describe teacher characteristics and teachingtechniques that research has shown to be effective. We are counting on you to tell us if youthink these statements describe Mr. Escalante and his teaching techniques. To the left of each statement is ashort blank line and all of the seventy-five short blank lines are in the left column under the heading called"Rating." Please first read each statement. For example, statement #1 says that Mr.Escalante "is well organized." Next, decide if you agree or disagree with the statement. For .xample,do you agree or disagree that he "is well organized?" If you agree, you will assign a rating of between+1 and +9, depending on how strongly you agree. If you disagree, you will assign a rating of between -1 and -9, depending onhow strongly you disagree. Please refer to the statement rating scale below when choosing the bestrating number. Please notice a rating of zero (0) means you are "Undecided" or "Neutral" while positive numbersbetween +1 and +9 indicate increasing degrees of agreement and negative numbers between -1 and -9 indicatevarious degrees of disagreement with the statement. For example, if you only slightly "agree" with a statement, youwould assign a "+1" rating to it. If you "very strongly agree," you would assign a "+9"rating to it. Please use the scale below to assign a rating to each of the seventy-five statements. Appendix D (Continued)

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Very Neutral Very Strongly Strongly or Strongly Strongly Ay ee Dt .6.4 : Disau ;. Di ..-A ee UndecidedAu :- A !!. 9 -9 -8 -7 -6 -5I -4-3 -2 -1 0 1 2 3 4 5 6 7 8

Rating Statement to be rated Mr. Escalante:

1)is well organized 2) presents math lessons clearly 3)is enthusiastic 4)is energetic 5)is "warm" emotionally toward me 6)is friendly toward me 7) expects me to achieve and do well in math 8)is considerate of me 9)is cheerful 10)is often funny or humorous 11)is an excellent mathematician 12)believes in me 13) helps me see myself as a "winner" 14) expects me to work hard 15) helps me plan and strive for excellence 16) gives me the help I need when I get "stuck" 17) gives me a lot of math problems to do 18) helps me enjoy math 19) has helped me become more interested in math. 20) has helped me set higher goals for myself inmathm 21) has helped me set higher goals for myself inlife 22) expects me to spend a lot of time on math 23) gives me math problems I can do if I paidattention during his lectures and did the assignments 24) has helped me plan further into the future than I everhave before 25) has helped me understand that I can becomequalified for any job I want 26) has helped me learn how to work hard andtake responsibility for myself 27) has helped me see that education is important 28) manages our in-class time efficiently sothat disruptions and wasted time are kept to a minimum 29) has helped me understand that I as a learnerneed to be active not passive 30) has helped me see that I can control my owndestiny Appendix D (continued)

31) understands what my life at home is like 32) understands the world I will face after high school 33) has tried to get my parents to become involved and supportive of my school work 34)refers back to my prior knowledge when introducing new concepts 35)lets me know quickly whether I did a math problem correctly or not 36)lets me know quickly why I got a math problem wrong and what I should have done and why 37) has taught me to estimate answers to math problems so that I can reject unreasonable answers and know when an answer is "in the ballpark" 38) has helped me learn how to think through a word problem before I begin working onit; to analyze the challenges I face and explore alternative strategiesbefore I start to work 39) has guided me through the thinking processes I need to understand inorder to work word problems correctly 40) has given me frequent practice in doing word problems 41)refers back to experiences I have already had when he introduces new concepts 42) calls attention to diagrams, graphs, photos or illustrations that not only relate tothe lesson but also help me learn and remember 43) expects that I can and will learn a lot of math 44) rewards slower learners for their progress and effort 45) requires that faster learners put forth effort too; he won't let them just"coast" 46) has taught me rules and principles and the conditions under which they apply soI can solve math problems 47) captures and holds my attention 48) sequences what we cover in class so that my knowledge builds on itself andI am ready for the next step 49) monitors each student's progress so that all of us are actively engaged inlearning no matter how fast we learn 50) manages classroom time well by keeping wasted time and misbehavior to aminimum 51) works personally with students to help them cope with especiallydifficult life situations 52) takes us through the steps needed to solve a problem and explainsthe purpose of each step 53) encourages me to try harder by reminding me that people beyond ourschool are paying attention to how well we do 54) praises successful aspects of my work and gives me detailed recommendationsfor how I can improve 55) provides me access to a math tutor whose assistance has helped me 56) has helped me memorize math facts by teaching highlystructured and carefully sequenced lessons with feedback from him when I get correct answers 57) has helped me achieve more by asking both factual and morecomplex, thought- provoking questions 58) has helped me develop better study skills 59) gives me homework that is useful, is an important partof classroom instruction, is evaluated by him and counts toward my grade 60) monitors my progress frequently and systematically 61) helps me see how new information relates to old information wehave already covered Appendix D (continued)

62) has encouraged public recognition for students who succeed and promoted a sense of school pride 63) has promoted agreement by the principal, teachers, students, and parents onthe goals, methods, subjects and topics to be taught 64) puts academics first 65) believes my first priority is to learn 66) expects and rewards my academic success 67) expects me to be honest, courteous, and to show respect for others 68) expects me to attend class, come to class on time, and meet the assignmentdeadlines 69) enforces discipline policies consistently and fairly 70) works with other math teachers at Garfield High to develop math related goalsthat emphasize student achievement 71) has helped me understand that I learn more in rigorous, tough courses thanin courses that are easier 72) has helped me see the advantage of advancing in math at a faster pace byattending summer school 73) encourages me to get involved in extracurricular activities to round out my education 74) would much rather I not take a part-time job that would require 15 hours or more per week of my time 75) has helped me understand that employers will want me to have a solidpreparation in math, reading, writing, and problem solving 76) Of the 75 teacher descriptions and actions noted above, some are probably moreimportant to you than others. Please review items 1-75 aboveand identify the "top ten" that are most important to you. Do this by putting a circle around u - item number ofeach statement that you judge to be one of the "top ten" most important.For example, if you judge statement #5 above as one of your "top ten," just circle the number "5." Keep circling statementnumbers until you have circled ten.

77)During the nine months you attend Garfield high, you spend about an hour each day,Monday through Friday, in Mr. Escalante's math class. Given that you spend aboutfive hours a week on "in-class work," we want to know how manyhours you spend outside of class working on "homework" for just his class. Pleasewrite your answer in the blank below. (Note: If you return to his classroom afterschool in the afternoon, write in the following blank the number of hours per week this is.I spend hours per week working on math in the afternoon. If you also go to ELAC on Saturdays, write in the following blankthe number of hours per week this is. I spend hours per week working on math on Saturdays. Be sure you add your afternoon hours to yourELAC Saturday hours together with regular homework hours to get the total you write in the blank below.)

I spend an average of total hours per week on homework for Mr. Escalante's class. 78) How many hours per week do you spend watching television?

I spend an average of hours per week watching television.

99 1; ?, Appendix D (continued)

79) My success or failure in doing a math problem correctly is due mainly to: a) my effort b) my ability c) my effort and ability d) my good luck if I get it right, my bad luck if I get it wrong e)the fact that the problem was either too easy, so I got it right; or toohard so I got it wrong 80) Can you think of other things Mr. Escalante does or other ways todescribe him that explain how he helps you? If so, please list them below. If youthink one or more of these are as important as those you identified as being among your "top 10" mostimportant, please number them as "11", "12", "13", etc. , and we will add them to your"top 10" list..If they are not that important, please just listthem and identify them as "a," "b," "c," etc.

81)Is there anything else you would like to sayabout Mr. Escalante or what it is like to be his student? If so, you may write on the back side of this page.

100 1 Appendix E Responses of Calculus Students to One Question on the Appendix C Questionnaire n = 47

76) 0; the seventy-five teacher descriptions and actions noted above, some are probably more important to you than others. Please review items 1-75 above and identify the "top 10" that are mostimportant to you Do this by putting a circle around the item number of each statement that youjudge to be one of the "top 10" most important For example, if you judge statement #5 above as one of your "top 10," just circle the number "5." Keep circling statement numbers until you have circled ten.

Number of Times # Item Identified 21)has helped me set higher goals for myself in life 19 27)has helped me see that education is important 15 53)encourages me to try harder by reminding me that people beyond our school are paying attention tohow 15 well we do 64)puts academics first 15 65)believes my first priority is to learn 16 3) is enthusiastic 14 47)captures and holds my attention 14 13)helps me see myself as a "winner" 13 51)works personally with students to help them cope with especially difficult life situations 13 10)is often funny or humorous 12 32)understands the world I will face after high school 12 7) expects me to achieve and do well in math 11 14)expects me to work hard 11 26)has helped me learn how to work hard and take responsibility for myself 11 30)has helped me see that I can control my own destiny 11 68)expects me to attend class, come to class on time, and meet the assignment deadlines 11 75)has helped me understand that employers will want me to have a solid preparation in math,reading, 11 writing, and problem solving 4) is energetic 10 11)is an excellent mathematician 10 2) presents math lessons clearly 9 12)believes in me 9 25)has helped me understaad that I can become qualified for any job I want 9 1) is well organized 8 15)helps me plan and strive for excellence 8 16)gives me the help I need when I get "stuck" 8 20)has helped me set higher goals for myself in math 8 24)has helped me plan further into the future than I ever have before 8 42)calls atteation to diagrams, graphs, photos or illustrations that not only relate to the lessonbut also 8 help me learn and remember 71)has helped me understand that I learn more in iigorous, tough courses than in coursesthat are easier 8 72)has helped me see the advantage of advancing in math at a faster pace by attending summerschool 8 8) is considerate of me 7 7 36)lets me know quickly why I got a math problem wrong and what I should have doneand why 43)expects that I can and will learn a lot of math 7 46)has taught me rules and principles and the conditions under which they apply soI can solve math 7 problems 49) moniton each student's progress so that all of us are actively engaged in learning no-matterhow fast we 7 learn 7 62)has encouraged public recognition for students who succeed and promoted a senseof school pride

101 126 Appendix E (continued)

Number of Times # Item Identified

66)expects and rewards my academic success 7 5) is "warm" emotionally toward me 6 22)expects me to spend a lot of time on math 6 31)understands what my life at home is like 6 38)has helped me team how to think through a word problem before I begin working onit; to analyze the 6 challenges I face and explore alternative strategies before I start to work 59)gives me homework that is useful, is an important part of classroom instruction, is evaluatedby him 6 and counts toward my grade 6) is friendly toward me 5 18)helps me enjoy math 5 19)has helped me become more interested in math 5 23)gives me math problems I can do if I paid attention during his lectures and did the assignments 5 29)has helped me understand that I as a learner need to be active not passive 5 67)expects me to be honest, courteous, and to show respect for others 5 9) is cheerful 4 37)has taught me to estimate answers to math problems so that I can reject unreasonable answersand know 4 when an answer is In the ballpark" 40)has given me frequent practice in doing word problems 4 45)requires that faster learners put forth effort too; he won't let them just "coast" 4 52)takes us through the steps needed to solve a problem and explains the purpose of each step 4 57)has helped me achieve more by asking both factual and more complex, thought-provokingquestions 4 17)gives me a lot of math problems to do 3 28) manages our in-class time efficiently so that disruptions and wasted time are kept to aminimum 3 33)has tried to get my parents to become involved and supportive of my school work 3 35)lets me know quickly whether I did a math problem correctly or not 3 48) sequences what we cover in class so that my knowledge builds on itself and I am ready for the next step 3 50) manages classroom time well by keeping wasted time and misbehavior to aminimum 3 54)praises successful aspects of my work and gives me detailed recommendations forhow I can improve 3 55)provides me access to a math tutor whose assistance has helped me 3 73)encourages me to get involved in extracurricular activities toround out my education 3 39)has guided me through the thinking processes I need to understand in order towork word problems 1 correctly 41)refers back to experiences I have already had when be introduces new concepts 1 58)has helped me develop better study skills 1 2 34)refers back to my prior knowledge when introducing new concepts 2 60)monitors my progress frequently and systematically 2 61)helps me mellow new information relates to old information we have alreadycovered 2 63)has promoted agreement by the principal, teachers, students, and parents onthe goals, methods, subjects and topics to be taught 2 69)enforces discipline policies consistently and fairly 2 70)works with other math teachers at Garfield High to develop math relatedgoals that emphasize student achievement 2 74)would much rather I not take a part-time job that would require 15 hours or more perweek of my time 0 44)rewards slower learners for their progress and effort 0 56)has helped me memorize math facts by teaching highly structured andcarefully sequenced lessons with feedback from him when I get correct answers

102 Appendix F Responses of Calculus Students toTwo Open-Ended Questions onthe Questionnaire in Appendix C n = 47 80) Can you think of other thingsMr. Escalante does or other ways todescribe him that If so, please list them below.If you think one or more explain how he helps you? identified as being among your "top 10" most of these are as important as those you and we will add them to important,please number them as "II", "12","13", etc., your "top 10" list.If they are not that important,please just list them and identify them as "a," "b," "c," etc. helpful. He is very nice and encow ages everyonewell. He teaches us a lot of stuff that is He is creative, hum) , conventional inmethods of teaching. a . quitting. b. He makes us believe we can strive forexcellence as long as we strive for it without c. Keeps a hectic schedule, yet attends tostudents' needs and fulfills his teaching requirements. 11. He encourages us, as Mexicans, to gofor the best. We are as good as anyone.

11. Makes you feel good about yourself. 12.Makes math interesting and challenging. Makes you see yourself as a winner. 13. and 14.Makes you feel (believe) that you can doanything with hard work determination "CANAV

a . He spends extra hours after schoolhelping the students who need extra help. He's not only a teacher but also a friend that manystudents can confide in. b. while and c. He makes the class more interestingby letting us play games once in a bringing us cookies or snacks to munch on.

11. By pushing you further beyondthe point where you quit and stoppedtrying. 12.By believing in you when no one elsewill give you a chance. 13.By giving examples you are capableof understanding. a . By never letting you quit and finding youif you do decide to quit along Escalante knows and understands us. A factorof his success is that he has the ability to get with people. He's more than ateacher, he's a friend. a.If I don't undersWid it the first time,he should use another method. b. Thanks to him, I have seen a successful personthat attended Garfield. all the school days to help or when wereally need him. c. Too bad that now he can't be in class d. Mr. Escalante is very good in helpingother teachers. 11. He will let us find out mistakesbefore we can go to him for help. there willing to help me. He He listens to my personal problems.He gives me advice. He is always is more than a math teacher.

1 2S 103 Appendix F (Continued)

a . He helps us get money into our program for better education. b. He supports us when we need to be supported.

11.He spends a lot of extra time with his students in which no monetary pay is given to him.

11.Has taught me never to give up and try hard. 12.Has also taught me that I can be whatever I want and that it's all up to me. 13.Everyone can be successful. There are no words to express his teaching but that he is the best teacher I ever had.He inspired me to be a better student, to study more, and to believe inmyself. He is the best there will ever be.

81)Is there anything else you would like to say about Mr. Escalante orwhat it is like to be his student?If so, you may write on the back side of this page.

1: really enjoyed being Mr. Escalante's student for the past two years and I'mlooking forward to be his .student again next year. A good and excellent teacher that Garfield should admire and thankfor his efforts!

Being a pupil ,)f Mr. Escalante is exciting and honorable. The class is neverdull; something new is always learned. The visitors and interviewers were helpful and interesting.I consider Kimo not just a teacher but a friend. To be Escalante's student was to be special. I don't have a father-figure athome and I'd say that. To me, Escalante was like a father to me. He isenergetic and enthusiastic about education, which is good. I not only learned about calculus in his class, I learned aboutlife as well. It was a wonderful experience being his student one which I will never forget. I willalways remember him.

It was definitely an experience having Mr. Escalante as my teacherbecause I was used to having teachers that were more serious in the class. But Escalante is a verygood teacher and he helps to motivate his students to strive for the best.

He would be a better teacher if he didn't take so many trips duringthe year.

He is a good teacher. His efforts to encourage students towork are great. He is a friend and a teacher.

To be in his class you have to have the desire.

I am honored to be a student of Mr. Escalante. Everyonehas an equal opportunity to excel in his classroom, but one must be willing to sacrifice their time.

Very proud to see a teacher so involved in teaching andshould be highly commended. He is a very encouraging teacher and inspiring. I would like to say something that if he leaves I'll keep oncalculating. Appendix G Responses of Calculus and Algebra II Students to ThreeQuestions on the Questionnaire in Appendix C n = 73

# Item Hours 77) Average number of hours per week working on math in the afternoon. 5.4 Average number of hours per week working on math on Saturdays. 2.7 Average number of total hours per week on homework for Mr. Escalante's class. 8.9

78) Average number of hours per week watching television. 7.7

# Item Percent 70) My success or failure in doing a math problem correctly is due mainly to: a)my effort 30.1% b) my ability 11.0% c)my effort and ability 57.5% d)my good luck if I get it right, my bad luck if I get it wrong 4.1% e)the fact that the problem was either too easy, so I got it right; or too hard, soI got it wrong 12.3%

Eh) 105 Appendix H Abstract Submitted Prior. to Paper Presentations Made at Conferences Held by The American Evaluation Association and the California Educational Research Association

1 His recent, extraordinary success in teaching advanced calculus to inner-citymostly Hispanic students in East Los Angeles has been chronicled not only in a book, Escalante.The Best Teacher in America, but also in a film, "Stand and Deliver." Beginning in 1989, the Escalante Mathematics Project was funded through a partnership involving grants from the National Science Foundation (NSF), ARCO, and FordMotor Corporation, as well as in-kind support from East Los Angeles College. The projectenabled "The expansion of the highly successful East Los Angeles CollegeAdvanced Placement Calculus program to include a second local high school, (and established) ... asupporting mathematics program for three feeder junior high schools." (ELAC, 1988, p. 3) The NSF grant application promised the production of an "InstructionalGuide" that would document "the body of techniques that make up the teaching and motivatingmethods of Jaime Escalante." (ELAC, 1988, p.2) At the 1990 AEA Conference in Washington,D.C., and the CERA Conference in San Diego, the approach taken to generate the InstructionalGuide was presented in a paper. Among other things, that approach involved asking Escalante'scalculus students, who had been with him for three or four years, to complete aquestionnaire in which they would rank each of 75 statements on teacher practices and attributes as more orless like him. Those statements had been derived from research findings found inthe following three sources: What Works: ResearchAbout Teaching and Learning (USDOE, 1989), Motivation: What Research Says Jo the Teacher (NEA, 1990). The statement judged to be mostlike him was, "Mr. Escalante is often funny or humorous"; the onejudged to be least like him was, "Mr. Escalante encourages me to get involved in extracurricularactivities to round out my education." (Kester, 1992) Two knowledgeable colleagues of Escalante, whohad observed him extensively in class, completed the same questionnaire.Finally, in a videotaped interview, Escalante was asked about the top thirty-eight (38) statementsfrom the list of those identified by his students: e.g., did he agree with or disagree with each statement,and what additional methods or practices did he use. The qualitative procedureof "data triangulation" was thus used to create the Guide, whichwill be available at AEA in Seattle and CERA in San Francisco.

106 Appendix Dr. Michael Scriven's Letter

MICHAEL SCRIVEN P.O. Box 69, Pt. Reyes, CA 94956 (415) 663-1511 'ReyesRidge' 415 Drakes View Drive, Inverness, CA 94937 FAX: (415) 663-1913 (24 hrs.)

January 12, 1993

Don Kester Los Angeles County Office of Education 9300 Imperial. Highway Downey, California 90242

Dear Don:

I'vejust had an opportunity to go throughalthough I didn't read every pageyour very valuable evaluation report on Jaime Escalante.

I'm so glad that you were able to do this; it is a very important documatt in the history of the study of teaching. I hope you've made arrangements to get it into ERIC for consideration; their selection process is very weird, but I suspect you wouldn't have much trouble getting it adopted.

I haven't really heard any authoritative news about how Jaime is doing in Sacramento. This is a Saturday, so I won't be able to reach you at the office and I'm off to the East tomorrow, but if you do hear of anything, a xerox to me would be much appreciated.

All the best for the new yearand it has been a pleasure to meet you and read the report.

MICHAEL. SCRI'VEN

MS:dlc

107 :cs) -\

Appendix J Mr. Jaime Escalante's Contract

Los Asa= Wins Som. Cirmaa, LEONARD N. IIRITION somoNors 1 a.A.Al Garfield High School MAMA TOISADO 5101 f. Sarni Man US ANCIANA CALAIDONIA NMI Ara* Tamale aU3) NNW

CONTRACT FOR ADVANCED PLACEMENTCALCULUS CLASSES As a requirement for enrolling in Mr. Escalante's Advanced Placement Calculus AB contract must be adhered to which stem and BC, a

We. the undersigned students, parents and teachersagree to abide by the followinr 1. The student understands that this isa one year, college-level class. Therefore and D's and Fail's are not acceptable. grades of C's

2.Every studentwillbring GANASto the class which is essential if heor she is to be successful irethis class.

3. The student, through theyearwillbuild up his or her confidence in the understand that calculus is merely subject and come to a name and that the subject can be fun. Studentswill notbe restricted in the number or questions that theycan ask, even if they appear to be simple. 4. The student agrees to be on time as there is a short quiz daily at the beginningof the period. The regular test day is Friday.lf a student is to be successful he homework that is assigned. or she must do the daily

5. The parents agree to cooperate with the teacher and give as muchsupport to their son or daughter as possible by encouraging themto do 1 1/2 of hours or study every night. 6. The student agrees to come after school for help if necessary (Room MH-1)whenever he or she does not understand assignments. Noexcuses will be accepted as the teacher will be available every day.

7. The parents agree that their son or daughter must come Saturdays to East LosAngeles Col- lege to prepare for the SATtest, and catch up with whatever has not been fast and lunch will also be served. completed. Break-

E. The student agrees to take care of the materials, not to destroy privateproperty, and in general help to maintain a learning environment.

9. The teacher also agrees toc.,.gr s to school withCAMAS,and in a good frame of mind every- day. He will take the responsibility for making the course as easy as possible. Hewillattempt to to make each student as knowledgeable as possibleabout calculus so that he or she can be successful in the AP Calculus exam.

10, The teacher agrees to maintain contact with the parents and inform them of theirson or daughter in the course. He will makeevery effort to develop the full potential of each student.

STUDENT DATE PARENTS DATE TEACHER DATE

108 1 '.13